TM 5-858-6
TECHNICAL MANUAL
DESIGNING FACILITIES
TO RESIST
NUCLEAR WEAPONS EFFECTS
HARDNESS VERIFICATION
HEADQUARTERS, DEPARTMENT OF THE ARMY
AUGUST 1984
AUTHORIZATION/RESTRICTIONS
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public property and not subject to copyright.
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Reprints or republications of this manual should include a credit substanially as follows: "Department of
the Army, USA, Technical Manual TM 5-858-6, Designing Facilities to Resist Nuclear Weapons Effects,
Hardness Verification."
If the reprint or republication includes copyrighted material, the credit should also state: "Anyone wishing
to make further use of copyrighted material, by itself and apart from this text, should seek the necessary
permission directly from the proprietor."
TECHNICAL MANUAL
No. 5-858-6
TM-5-858-6
HEADQUARTERS
DEPARTMENT OF THE ARMY
Washington, DC, 31 August 1984
FACILITIES TO RESIST
NUCLEAR WEAPONS EFFECT
VERIFICATION
Chapter 1. INTRODUCTION
Introduction 1-1 1-1
TM 5-858-6: Hardness Verification 1-2 1-1
Chapter 2. GENERAL METHODOLOGY
Introduction 2-1 2-1
Indentification and Organization of Systems Elements 2-2 2-1
Weapons-Effect Loads 2-3 2-2
Quantifing Resistances 2-4 2-2
Chapter 3. STATISTICAL PROCEDURES
Introduction 3-1 3-1
Probabilistic Distribution 3-2 3-1
Analysis for Resistance 3-3 3-2
Mean and Variance by Normal, t, Distribution 3-4 3-2
Nonparametric Distributions 3-5 3-6
Binomial Distributions 3-6 3-10
Chapter 4. VERIFICATION REQUIREMENTS AND EXPERIMENTAL METHODS
Introduction 4-1 4-1
Simulation Requirements 4-2 4-1
k Simulating and Testing Overpressure 4-3 4-3
m Simulating and Testing Ground Shock 4-4 4-5
* Simulating and Testing EMP 4-5 4-13
Chapter 5. ANALYTICAL TECHIQUES
Introduction 5-1 5-1
Computing Uncertainties and Surviviability 5-2 5-1
Types of Analytic Techniques 5-3 5-1
The Monte Carlo Method 5-4 5-2
Engineering Judgement 5-5 5-2
Direct Differentiation of Functions 5-6 5-4
Chapter 6. VERIFICATION METHODOLGY
Introduction 6-1 6-1
Diagrams, Network Logic, Fault Trees, and Boolean Algebra 6-2 6-1
Elements of Verification Analysis 6-3 6-4
Correlations 6-4 6-4
Appendix A.
Appendix B.
Appendix C.
Glossary
Binomial Distribution
Techiques for Simulation Testing
Bibliography
A-l
B-l
C-l
G-l
"This manual together with TM 5-858-1; TM 5-858-2; TM 5-858-3; TM 5-858-4; TM 5-858-5; TM 5-858-7; and TM 5-858-8
supersedes TM 5-856-1, 1 July 1959; TM 5-856-2, 15 March 1957; TM 5-856-3, 15 March 1957; TM 5-856-4, 15 March 1957; TM
5-856-5, 15 January 1958; TM 5-856-6, 15 January 1960; TM 5-856-7, 15 January 1958; TM 5-856-8, 15 January 1960; and TM
5-856-9, 15 January 1960.
i
LIST OF FIGURES
Figure Page
3-1 Operating Characteristics Curve for Different Values of n for the Two-sided t Test for a
Level of Significance a=0.05 3-7
3-2 Operating Characteristics Curve for Different Values of n for the One-sided t Test for a
Level of Significance a=0.05 3-8
3-3 Percentage of Population Within Sample Range as a Function of Sample Size 3-9
3-4 Percentage as a Function of Sample Size and Probability 3-12
3-5 Determination of Minimum Sample Size (Pi/p vs. s/n) 3-15
3-6 Lower (p t ) of the Proporation of Survivals to be Expected, Resulting from s Successes in
n Tests 3-17
4-1 Sketch of HEST Facility 4-4
4-2 Typical HE Field Test Configuration (Spherical Charge) 4-7
4-3 The Giant Reusable Airblast Simulator (GRABS) 4-6
4-4 Large Blast Load Generator (LBLG) 4-8
4-5 Regions under Test Bed where Peak Vertical Velocity, Stress, and Acceleration can be
Attained Without Edge Interference 4-10
4-6 HE Test Configuration to Simulate Crater-Induced Ground Shock 4-11
4-7 HEST/BLEST T Configuration 4-12
4-8 Typical HEST/DIHEST Test Array 4-14
6-1 Types of logic diagrams 6-2
6-2 Typical generalized fault tree 6-3
6-3 Typical Fault Tree with Network Logic Symbols 6-5
6-4 Loads, Transfer Functions, and Resistance ; 6-6
ii
LIST OF TABLES
Figure Page
3-1 Percentage Points of the t Distribution 3-3
3-2 The X 2 Distribution 3-11
4-1 Protective Systems: Requirements for Weapon-Effect Hardness Verification 4-2
A-l Individual Terms Probability of Realizing s=r Successes in n Trials A-l
A-2 Partial Sums Probalility of Realizing s>r Successes in n Trials A-10
B-l Dynamic Pressure Tests Using Shock Tubes to Simulate Airblast Effect B-2
B-2 Ground Shock Using Blast Load Generators to Simulate Airblast Effects* B-5
B-3 Dynamic Loading of Material Using Special Test Machines to Simulate Airblast Effect B-6
B-4 Full Scale Soil Loading Tests of Airblast Effect During Field Tests B-8
B-5 Dynamic Water Wave and Shock Tests, Simulating Airblast on Direct Shock B-9
B-6 Blow-Off Response Using Sheet Explosives to Simulate Nuclear Radiation Effect B-9
B-7 Tests of Nuclear Radiation Effects A-10
B-8 Tests of Thermal Radiation Effects A-10
B-9 Tests of EMP Effects B-ll
B-10 Chronology of HEST and DIHEST Tests B-14
B-ll Chronology of High-Explosive Tests B-16
B-12 GRABS Tests: Giant Reusable Airblast Simulator B-18
1
INTRODUCTION
1-1. General.
a. This series of manuals, entitled Designing Fa-
cilities to Resist Nuclear Weapon Effects, is or-
ganized as follows:
TM 5-858-1 Facilities System Engineering
TM 5-858-2 Weapon Effects
TM 5-858-3 Structures
TM 5-858-4 Shock Isolation Systems
TM 5-858-5 Air Entrainment, Fasteners,
Penetration Protection,
Hydraulic-Surge Protective
Devices, EMP Protective
Devices
TM 5-858-6 Hardness Verification
TM 5-858-7 Facility Support Systems
TM 5-858-8 Illustrative Examples
A list of references pertinent to each manual is
placed in an appendix. Additional appendixes and
bibliographies are used, as required, for documen-
tation of supporting information. Pertinent biblio-
graphic material is identified in the text with the
author's name placed in parentheses. Such biblio-
graphic material is not necessary for the use of
this manual; the name and source of publications
related to the subject of this manual is provided
for information purposes.
b. The purpose of this series of manuals is to
provide guidance to engineers engaged in designing
facilities that are required to resist nuclear weapon
effects. It has been written for systems, structural,
mechanical, electical, and test engineers possessing
state-of-the-art expertise in their respective dis-
ciplines, but having little knowledge of nuclear
weapon effects on facilities. While it is applicable
as general design guidelines to all Corps of En-
gineers specialists who participate in designing
permanent military facilities, it has been written
and organized on the assumption a systems-
engineering group will coordinate design of the
facilities.
c. Technical Manual 5-858 addresses only the de-
signing of hardened facilities; other techniques to
achieve survival capacity against nuclear weapon
attacks are deception, duplication, dispersion,
nomadization, reconstitution, and active defense. A
facility is said to be hardened if it has been de-
signed to directly resist and mitigate the weapon
effects. Most of the hardening requirements are
allocated to the subsidiary facilities, which house,
support, and protect the prime mission
materiel/personnel (PMMP). This manual is ap-
plicable to permanent facilities, such as those asso-
ciated with weapon systems, materiel stockpiles,
command centers, manufacturing centers, and com-
munications centers.
d. The nuclear weapon threats considered are
listed below. Biological, chemical, and conventional
weapon attacks are not considered.
Weapons aimed at the facility itself or at
nearby targets
A range from many, relatively small-yield
weapons to a single super-yield weapon
Weapon yields from tens of kilotons to
hundreds of megatons
Weapon delivery by aerial bombing,
air-to-surface missile, surface-to-surface
missile, or sattelite-launched vehicle
Detonation (burst) of a weapon in the air, at
the ground surface, or beneath the ground
surface
Direct-overhead bursts for a deep-buried
facility
Near-miss bursts for a near-surface facility,
producing peak over-pressures from tens
to thousands of psi at the facility
e. The designing of facilities resistant to nuclear
weapon effects is an evolving speciality using a
relatively narrow data base that incorporates both
random and systematic uncertainities. The range of
these uncertainties may vary from significant
(order of 1 to 2 magnitudes) to normal (10 to 100
percent variation from average values). The ap-
plicable uncertainity value depends on the specific
weapon effect or hardening objective under consid-
eration. Loading uncertainity is generally more sig-
nificant than resistance uncertainty. Awareness of
the appropriate uncertainty (extent of ignorance)
factor is essential not only for system engineering
trade-offs, but in the utilization of available analy-
sis or test procedures. Studies and experiments are
being conducted to improve methodology, to better
define random uncertainties, and to reduce system-
atic uncertainties. This manual will be revised as
significant improvements occur in either method-
ology or data base.
1-2. TM 5-858-6: Hardness
verification.
This volume presents methodology for verifying
the hardness of the facilities. The methodology
comprises both physical and mathematical simula-
tions. A synopsis of available testing facilities is
given.
1-1
2
2-1. Introduction.
a. A hardness verification program for protective
facilities and their systems, subsystems, and ele-
ments measures the ability to survive an attack
that has been specified in terms of weapon size,
range, and burst conditions and of particular site
characteristics. When nuclear test ban treaties pre-
cluded atmospheric nuclear testing, alternative
testing techniques and analytical procedures were
developed to assess the probability of a facility
surviving a prescribed attack. Most protective fa-
cilities are extremely complex, containing major
systems that require methodical testing at the sub-
system level and integration of the results; this
analytical methodology is called hardness verifica-
tion.
6. Hardness verification must be made at regular
intervals during the facility develop-
ment/design/construction cycle. Simple
verifications will be performed during the initial
design phases. As designs become firm and fabrica-
tion begins, more comprehensive verifications will
be made. It is essential that hardness verification
be used periodically to monitor the iterative pro-
cess of definition, systhesis, design (redesign), ana-
lysis, test, and evaluation that transforms mission
requirements to demonstrable and acceptable fa-
cility survivability. This will secure continuing in-
tegrity between design and construction, will verify
that each element, subsystem, and system has been
combined in a manner that properly accounts for
uncertainties in responses and the interdependence
of various physical parts of the facility.
c. The analyst must know the failure modes and
resistances for the relevant elements of the sub-
system or higher level assemblages, and the local
weapon-effect loads on those points. Whether from
experimental tests or from analyses, the data pro-
vided must include uncertainties associated with
each mean value. This volume deals primarily with
procedures to evaluate failure modes and resis-
tances; techniques to deal with the random nature
of the process are discussed in chapters 5 and 6.
2-2. Identification and organization of
system elements.
a. The first task in system hardness verification
is to define the physical system. The relationship
of each element to mission critical functions must
be accurately defined and the associated local loads
and failure modes must be specified. For complete
examination of a facility, network logic analysis
including the use of Boolean algebra is strongly
recommended. The construction of fault trees
within the context of multilevel system organiza-
tion is a procedure will suited to the solution of
complex problems dealing with verification activi-
ties.
6. The fault-tree approach provides for the analy-
sis of all elements, subsystems, and systems, and
includes every factor that influences the hardness
(or failure) of each element and consequently each
subsystem and system. It graphically represents
the logic that relates the failure mode(s) of system
elements to a particular weapon effect(s). That is,
the fault tree organizes failure-mode/weapon-effect
combinations into a logic network, thereby allowing
use of probabilistic information in descriping the
hardness of each element, subsystem, and system.
c. The multilevel system organization views the
protective facility as a hierarchy of systems, sub-
systems, and elements:
Level 1: Complete Faciltiy
Level 2: Complete Sytems
Level 3: Subsystems within Complete Systems
Level 4: Elements within Subsystems
(1) System Level 1 represents the finished fa-
cility, complete with protective and protected sys-
tems.
(2) System 2 includes complete functional sys-
tems that make up a particular facility. Included in
this category are both the protective and the pro-
tected systems. There are generally nine protective
systems:
Structure
Shock isolation
Air entrainment
Anchors, mounts, and fasteners
Penetration
Hydraulic-surge protective devices
EMP protective devices
Radiation shielding
Thermal shielding and fire barrier
The protected systems include:
Power supply
Power distribution
Cooling
Heating and ventilation
Water supply
Sewage disposal
Lighting
Communication
Prime-mission materiel
Personnel
2-1
TM 5-858-6
If required by the facility mission, other protected
systems may also exist in the facility.
(3) System Level 3 includes the complete func-
tional subsystems that make up a system. For ex-
ample, the various subsystems of the air-
entrainment system are:
Intake structure
Expansion chamber
Blast attenautor
Blast valve
Delay line
Filtration
(4) System Level 4 includes the components of
the various subsystems. For example, the blast
valve subsystem of the air-entrainment system
would have components such as:
Valve hardware elements
Attachment hardware parts
Actuation components
Sensor elements
d. Typical hardened facilities will include thou-
sands of structure and equipment items. It is im-
practical and unnecessary to verify the hardness of
each item. The analyst must define some consistent
method for the selection (or screening) of items.
The specifics of the method may differ from sys-
tem to system, but a fairly universal approach
includes these four basic steps:
(1) Identify those items of equipment that are
critical mission success. (Note: the noncrit-
ical items must not pose a threat to the
critical items when damaged or destroyed
during attack.)
(2) Identify those critical items that are suscept-
ible to the weapon effect.
(3) Identify those items that have marginal
hardness. Omit items having a large factor
of safety. List items that obviously will fail
and must be redesigned.
(4) From each population of different items re-
miaining, randomly select a statistically sig-
nificant sample for test or perform probabil-
istic computations to verify hardness.
2-3 Weapon-effect loads.
a. After the items have been selected for ver-
ification, identify local loads induced by one or
more of the free-field nuclear weapon-effect envi-
ronments. Identify the total signal path and path
segments leading from the free field to the ele- M
ment. Determine the transfer function for each I
path segment. In some instances, the inputs to be ^
used for hardness verification will be the same as
those used for design purposes; in other instances,
the inputs will be determined by extensive testing
and analytic programs.
b. Identifying the total transmission path is best
performed by applying network logic analysis
(chap. 6).
c. Determining transfer functions is the process
of relating free-field nuclear environments to local
loads in order to assess hardness levels. Transfer
functions may be determined experimentally; more
often, an analytical procedure will be employed.
2-4. Quantifying resistances.
a. The resistance of a system, subsystem, or ele-
ment is defined as its ability to withstand nuclear
weapon-effect loads. The load-resisting characteris-
tics may be quantified by experimental data
(laboratory or field) or by analysis of mathematical
models. Scarcity of experimental data may require
augmentation from computational models to accrue
a statistically significant body of data.
b. Data from either laboratory or field tests are m
preferred for determining resistance. Tests can be
conducted on prototypes or scale models; but in
order to be statistically meaningful, a significant
number of tests must be conducted. (See chap 3 for
the statistical implications of testing; see chap 4
for the types of tests available.) If testing is not
possible because of technical difficulties or lack of
equipment, time, or funds, a computational analysis
will be required.
c. Analytical procedures, especially numeric tech-
niques, are the backbone of many of the verifica-
tion studies applied to hardened systems. Although
deterministic analytical procedures have reached
an advanced state of development, probabilistic
analyses that allow for the computation of uncer-
tainties and survival problbilities are markedly less
familiar. Thus, the performance of verification
analyses according to the guidelines in chapter 6
will require considerable ingenuity. Some guide-
lines to the development of probabilistic procedures
that can be applied to real systems are presented
in chapter 5.
2-2
3
3-1. introduction.
a. Statistical techniques are usually associated
with laboratory testing. Application of these tech-
niques to field testing, and especially to the statis-
tical inferences of calculations, is still in an early
state of development; consequently, the verificaiton
anslyst will not have the benefit of extensive pre-
vious work.
b. Hardness verification is performed to answer
either of two basic survivability questions: (1) How
hard is the system? or (2) Is the system hard to a
specified level? In answering question (1), the re-
sistance to pertinent weapon effects is determined.
This provides a more generally comprehensive and
useful answer. Then, if the mean resistance is de-
termined to be greater than the mean specified
hardness goal, the answer to question (2) is auto-
matically (and deterministically) "yes"; if it is de-
termined to be lower, the answer is "no." In a
properly designed system, however, a deterministic
"yes" is not inconsistent with a probabilistic "no"
and vice versa; there is some probability that a
system will fail (or survive) regardless of its most
probable behavior.
c. Hardness verification generally is not
conducted to answer Question (1) because it is
much more costly to determine what the resistance
is than it is to determine whether the resistance is
above or below some specified level. If undertaken,
the result will be a mean resistance with a cor-
responding variance or uncertainty for each
weapon-effect failure-mode combination. By com-
bining the resistance for all t modes of failure, the
mean-resistance/uncertainty for a particular sys-
tem or subsystem will be determined.
d. Verification analysis to answer question (2)
will result in a hardness statement that presents
the probability of success (probability of the par-
ticular failure-mode resistance being equal to or
greater .than the stated hardness goal) with a cor-
responding level of confidence (e.g., there is a 90
percent probability that the resistance is >800 psi,
with a confidence of 70 percent.)
e. Throughout design and development of the
hardened system, it is important to acquire . re-
sponse data to identify failure modes. If possible,
avoid "go/no-go" tests restricted to a single level in
order to minimize retesting downstream as ele-
ments of the prototype design are changed.
f. The hardness statement must have statistical
validity regardless of the point of view taken in b
above. A purely deterministic statement will, not
be acceptable unless the system, subsystem, or ele-
ment is superhard or supersoft.
3-2. Probabilistic distribution.
a. Ask the following questions: Is it necessary to
define a specific type of distribution? If so, what
type of distribution should be selected?
b. For many (if not all) of the analyses to be
conducted, the definition of the exact distribution
will not critically affect the results. (See Aitchison-
Brown, 1969; Benjamin-Cornell, 1970.) This is true
for the following circumstances:
If the distribution is not grossly nonlinear
near the mean
If the uncertainty parameter 2 = -~ is small
(i.e., Q 2 1.0) M
where
<r =The true standard deviation
M =The true mean
These assumptions are equivalent to ignoring the
tails of the distribution (i.e., at those responses
exceeding, say, 30"). These assumptions will al-
most always be acceptable for verification analyses.
Furthermore, the normal or log normal distribu-
tion will provide an adequate approximation in
most cases. Whether the normal or log normal
model is adopted because of physical considerations
or as an approximation to another distribution, it
will be sufficiently accurate in practical applica-
tions.
c. If a normal distribution cannot be adopted,
then either conduct enough tests (usually >30)
that the assumption of a particular distribution
can be defined (using, for instance, a chi square
goodness-of-fit test), or transform the data so that
the normal assumption may be made, or use a
distribution-free analysis. Others may be used, but
only if these are not suitable.
<L The normal, or t statistic, distribution is the
single most-used model in applied probability anal-
yses (Benjamin-Cornell, 1970). The normal distribu-
tion asymptotically represents the sum of a num-
ber of random events. For example, it represents
how a manufactured or constructed item deviates
from a specified performance value because of
flaws or errors in the many separate components
of the item. Therefore, the normal distribution is a
prime candidate to represent the random
3-1
TM 5-858-6
deviations of resistance from a specified level, since
this resistance nearly always results from a sum of
contributing components.
e. Adopt the normal distribution whenever as-
sumptions in b above can be accepted. Use it also
whenever adequate tests are available and the as-
sumption of normality is confirmed through a chi-
square (X 2 ) test. (The performance of the chi-
square test is described in most of the references
in statistics included in this volume.)
/ If the variables are known to result from the
multiplication of many effects (still assuming b
above), use the lognormal distribution instead of
the normal. However, when Q 2 1, there will be
no significant difference between the normal and
lognormal results. In this volume only the normal
(t) distribution is discussed; a complete discussion
of the lognormal distribution is presented by
Aitchison-Brown (1969).
g. Select the nonparametric distribution instead
of the normal when assumptions in b cannot be
accepted and another particular distribution cannot
be confirmed.
h. Select the binomial distribution only when
"fail or succeed" information is acquired through
tests at a specified level.
3-3. Analysis for resistance.
a. Experiments can be designed to determine the
resistance of a single weapon-effect/failure-mode
combination for a simple element, or of combined
resistance for a total system or complex subsystem.
In either case, conduct enough independent trials
or tests to statistically determine the resistance(s)
of interest, usually >30 samples.
6. In experimental verification it will not be pos-
sible to "exactly" identify the resistance of interest.
The best that can be done is to bracket the resis-
tance. Ideally, bracketing is done by starting the
testing at a level where design analysis has shown
there will be a high probability of success, and
then increasing the level in small increments- until
failure occurs. The resistance then lies between the
level where failure occurred and the level just be-
fore failure. Obviously, the smaller the incremental
change in load level, the more accurately the resis-
tance can be bracketed for the item. Generally,
pecify the resistance as the last level where suc-
ess occurred. If, however, large increments
greater than */4 of the resistance) must be used
ecause of costs, a higher level might be taken. But
ever specify a level more than one-half of the
icrement above the last level of success; and sup-
ort such a resistance level by rigorous analysis.
c. Because testing total systems is expensive, the
resistance of a total hardened system must usually
be determined by combining the results of many
element or subsystem tests. The resistance of an
element, subsystem, or system is always related to
one or more weapon-effect/ failure-mode combina-
tion^). It is critically important to adequately sim-
ulate the weapon effect of interest and accurately
measure the resulting repsonses.
d. The use of statistics in testing for resistance is
different than statistics used in calculating resis-
tance. For experimental verification, a number of
tests are performed on the system, subsystem, or
element to define its statistical performance. In
calculated verification, the mathematical model for
the system, subsystem, or element is deterministic
but its constitutive parpameters such as stiffness,
weight, and strength are allowed to have a statisti-
cal character so that for each selection of param-
eters chosen a unique response will be obtained.
The calculations that result will have much the
same character as test data that result from ex-
perimental verification.
3-4. Mean and variance by normal, t,
distribution.
a. Given a sample of n data (such as resistance
measurements), the sample mean value and vari-
ance are defined as
x==.
(3-1)
n
(3-2)
or
n
J- X. / \
T y (XX)
n 1 ' ^
(3-3)
where
n = Number of samples
s 2 ,s 2 = Sample variances
x = Sample mean
Xj = Individual sample values
Equation 3-3 is presented as a better estimate of
the variance for n :<30.
3-2
TM 5-858-6
Table 3-1. Percentage Points of the t Distribution
(Table of t a . v the 100 a percentage point of the t distribution
for v degrees of freedom [v = n - 1])
\
"X. a
I'^X
.40
.30
.20
.10
.050
.025
.010
.005
.001
.0005
1
.325
.727
1.376
3.078
6.314 12.71
31.82
63.66 318.3 636.6
2
.289
.617
1.061
1.886
2.920 4.303 6.965
9.925
22.33
31.60
3
.277
.584
.978
1.638
2.353
3.182
4.541
5.841
10.22
12.94
4
.271
.569
.941
1.533
2.132
2.776
3.747
4.604
7.173
8.610
5
.267
.559
.920
1.476
2.015
2.571
3.365
4.032
5.893
6.859
6
.265
.553
.906
1.440
1.943
2.447
3.143
3.707
5.208
5.959
7
.263
.549
.896
1.415
1.895
2.365
2.998
3.499
4.785
5.405
8
.262
.546
.889
1.397
1.860
2.306
2.896
3.355
4.501
5.041
9
.261
.543
.883
1.383
1.833
2.262
2.821
3.250
4.297
4.781
10
.260
.542
.879
1.372
1.812
2.228
2.764
3.169
4.144
4.587
11
.260
.540
.876
1.363
1.796
2.201
2.718
3.106
4.025
4.437
12
.259
.539
.873
1.356
1.782
2.179
2.681
3.055
3.930
4.318
13
.259
.538
.870
1.350
1.771
2.160
2.650
3.012
3.852
4.221
14
.258
.537
.868
1.345
1.761
2.145
2.624
2.977
3.787
4.140
15
.258
.536
.866
1.341
1.753
2.131
2.602
2.947
3.733
4.073
16
.258
.535
.865
1.337
1.746
2.120
2.583
2.921
3.686
4.015
17
.257
.534
.863
1.333
1.740
2.110
2.567
2.898
3.646
3.965
18
.257
.534
.862
1.330
1.734
2.101
2.552
2.878
3.611
3.922
19
.257
.533
.861
1.328
1.729
2.093
2.539
2.861
3.579
3.883
20
.257
.533
.860
1.325
1.725
2.086
2.528
2.845
3.552
3.850
21
.257
.532
.859
1.323
1.721
2.080
2.518
2.831
3.527
3.819
22
.256
.532
.858
1.321
1.717
2.074
2.508
2.819
3.505
3.792
23
.256
.532
.858
1.319
1.714
2.069
2.500
2.807
3.485
3.767
24
.256
.531
.857
1.318
1.711
2.064
2.492
2.797
3.467
3.745
25
.256
.531
.856
1.316
1.708
2.060
2.485
2.787
3.450
3.725
26
.256
.531
.856
1.315
1.706
2.056
2.479
2.779
3.435
3.707
27
.256
.531
.855
1.314
1.703
2.052
2.473
2.771
3.421
3.690
28
.256
.530
.855
1.313
1.701
2.048
2.467
2.763
3.408
3.674
29
.256
.530
.854
1.311
1.699
2.045
2.462
2.756
3.396
3.659
30
.256
.530
.854
1.310
1.697
2.042
2.457
2.750
3.385
3.646
40
.255
.529
.851
1.303
1.684
2.021
2.423
2.704
3.307
3.551
50
.255
.528
.849
1.298
1.676
2.009
2.403
2.678
3.262
3.495
60
.254
.527
.848
1.296
1.671
2.000
2.390
2.660
3.232
3.460
80
.254
.527
.846
1.292
1.664
1.990
2.374
2.639
3.195
3.415
100
.254
.526
.845
1.290
1.660
1.984
2.365
2.626
3.174
3.389
200
.254
.525
.843
1.286
1.653
1.972
2.345
2.601
3.131
3.339
500
.253
.525
.842
1.283
1.648
1.965
2.334
2.586
3.106
3.310
oo
.253
.524
.842
1.282
1.645
1.960
2.326
2.576
3.090
3.291
U.S. Army Corps of Engineers
TM 5-858-6
b. The optimum procedure for testing the hy-
pothesis that the mean of a normal distribution
has some specified value M = ^ ) is based on the t
test statistic, where:
(3-4)
c: The acceptance region for a two-sided proce-
dure (where the hypothesis is stated as = ) is
3-5
where t is calculated from equation 3-4 with & =^
and a is the level of significance for the test; i.e.
there is a probability of I a of accepting the
hypothesis M = ^o when it is true. The values of
V2,n-i are taken from tables of t statistics such as
table 3-1. By combining equations 3-4 and 3-5,
For resistance verification analysis, a should range
between 0.05 and 0.10. The smaller the value of a,
the larger the confidence interval. In the extreme
case it would be possible to have a probability of
0.9999 (1 a ) that the true mean falls in an
interval so large as to be meaningless. This is
particularly true for small n.
/ A second probability is called the Type II
error, which is denoted by /3. The analyst selects /3
to represent the probability of accepting the hy-
pothesis when it is considered important to detect
the value of the ratio (^ l fJL Q /cr, where cr= true
standard deviation of the population and is un-
known. In other words, /3 is the probability of
accepting the hypothesis H : M = /a when actually
)LC=/X!. The analyst must choose values of ^i and cr
such that the ratio (^ -^ ) is meaningful to the
analysis.
g. Once /3 and the ratio MI =M> O /O- have been
selected, operating characteristics curves such as
those shown in figures 3-1 and 3-2 can be used to
determine n. This procedure is illustrated by the
following example, for which three problems and
solutions are presented.
x to/2, n
Example:
Item
Air-entrainment port
closure
The values xt /2,n-rV5~ are the confidence
limits and bound the confidence interval. Equation
3-6 states that /x lies within the given confidence
interval. This statement will be true 1 -a fraction
of the time.
<L In many instances the analysis to determine
the resistance will require answering this question:
Is the resistance equal to or greater than a specific
value? This allows use of the one-sided procedure
based on the hypothesis: ^ = /x - I n this case, the
acceptance region is
t^-t.n.1
The hypothesis is accepted if equation 3-7 is satis-
fied, but is rejected otherwise. This procedure also
has the probability of 1 - a of accepting the hypoth-
esis when it is true.
e. As stated above, 1 - a is the confidence level or
the probability of accepting the hypothesis when it
is true. Conversely, the probability of rejecting the
hypothesis when it is true is given by a. This is
called a Type I error. The value of a is selected by
the analyst, using input from the systems manager.
Weapon Effect
Failure Mode
Resistance Design Goal
Problem 1:
Calculate
AirblaSt
Stress
Pressure wave:
Rise time (t r )
= 0.002 sec
Max. pressure (P m )
= 1000 psi ( o
= 1000 psi, e.g.)
Decay time (t d )
=0.100 sec (time
to decay to P m /2)
The closure was designed to resist
1000 psi. Can the design be considered
successful at a level of significance of,
say, a. =0.05? Four resistance values
have been determined.
x (mean value of sample)
x (variance of sample)
C.I. (confidence interval)
3-4
TM 5-858-6
Test Data x x =900 psi
x 2 =1100 psi
x 3 =950 psi
x 4 =1000 psi
900 + 1100+950 + 1000
(using equation 3-1)
987.5 psi
2 = L- V (Xi-x) 2 (using eq. 3-3)
n 1 ~^
=1 /(900-987.5) 2 +(1100-987.5) 2 +(950-987.5) 2
3 {
s=85.4 psi
987.5-1000
85.4
X2 =-0.29
(using eq. 3-4)
a/2=0.05/2=0.025
n-l=3
From table 3-1, t^, 3 = 3.182
Since -3.182 <-0.29 <3.182, the hypothesis that
M = 1000 is accepted at a =0.05
C.I. =987.5- 3.182 X~- to 987.5 + 182x-^=852
to 1123 psi. 2 Z
Therefore, it can be stated that the mean resis-
tance of the population lies between 852 psi and
1123 psi, with a confidence of of 95 percent that
the statement is true. (Had a: =0.10 been selected
for the analysis, then it could be stated that the
mean resistance of the population lies between 887
psi and 1088 psi, with a confidence of 90 percent
that the statement is true; and for a =0.20, the
C.I. =918 to 1057 psi.)
Problem 2: Can the mean resistance be considered
equial to or greater than 1000 psi with
a =0.05?
One-Sided Procedure:
The acceptance region is t >: t ain _!
From the example:
t =-0.29
a
n-1
0.05
3
From table 3-1: t .o 5 ,3 =2.353
Since -0.29 > 2.353, the hypothesis is accepted at a
level of a =0.05.
C.I. -X-
to
Or it can be considered that the C.I. has a lower
limit only:
(3-6,
=987.5 -
=887 psi
It can be stated that the mean resistance of the
population is equal to or greater than 88 psi, with
a confidence of 95 percent.
Problem 3: What is the value of /8 for the above
sample of n =4?
Two-Sided Procedure:
Let d=
=2.0 (from / above)
If it is assumed that is a reasonable estimate of
a, then
or = 85.4 psi.
Since MO =1000 psi, then AC i =2 X 85.4 +1000
= 1171 psi.
/3 gives the probability of accepting the hypothesis
that M =1000 when actually M =1171 (or 829). /3 is
found by using figure 3-1. The intersection of the n
=4 curve and the d =2 value shows that /? would
be approximately 0.244. Therefore, for the sample
tested there is a probability of 0.244 of accepting
M=1000 psi, when actually is could be as low as
829 psi or as high as 1171 psi.
One-Sided Procedure:
Let d
=2.0
Again, cr=85.4 psi
3-5
TM 5-858-6
A4 =829 psl
j8 is found by using figure 3-2. is seen to be
equal to approximately 0.25. Therefore, for the
sample tested there is a probability of 0.25 of ac-
cepting /x>:1000, when actually it could be as low
as 829 psi.
3-5. Nonparametric distributions*
a. Distribution-free methods are utilized when
the conditions specified in paragraph 3-26 do not
apply or if the data set does not readily fit any
other recognizable distribution.
6. Use of nonparametric methods requires the
same kinds of tests as the t statistic described
above. These tests would result in a measurement o
the resistance level. The nonparametric results as-
sert that a particular proportion (p) of the popula-
tion has failure thresholds falling within a certain
range. The statement has an associated confidence
level (P). Procedures for calculation of the mean
and variance are not defined.
c. Using this method, it can be stated with the
probability (P) of being correct that no less than a
particular proportion (p) of the population has fail-
ure thresholds between the maximum and mini-
mum value of the failure levels observed in a sam-
ple of n tests. As before, the probability (P) is the
level of confidence. The range between the maxi-
mum and minimum is analogous to the confidence
interval.*
<L Assuming that the distribution is continuous
and that x denotes the proportion of the population
values that falls within the maximum and mini-
mum values of any random sample of size n, the
distribution of x (see Fisz, 1963) is given by
f(x) =n(n-l)x n - 2 (l-x)
(3-8)
Then
P =1 -HP*- 1 +(N-l)p n
An approximation for n from equation 3-8 is
n ^ 0.24
~
1-p
+0.5
(3-9)
where
p =The proportion of the population that will
fall within the sample range
Xj4 =The chi-square distribution for 4 degrees
of freedom
3-6
I a =The confidence level (a is the level of
significance)
Equation 3-9 is plotted in figure 3-3 for selected
values of P =1 a.
*The interval between any two observations may be used as
a confidence interval, but here only the sample range is dis-
cussed, of Sample Size
e. Analyses can also be performed based on the
distribution of exceedances. Some significant infer-
ences can be made from limited sample sizes. Har-
ris (1952) develops the equation
p = i_(i_ p )n
where P is the probability that in a future very
large sample, the proportion p or less of the ob-
servations will fall below the minimum value *
observed in a trial sample of size n. (It is also the
proportion that will exceed the maximum value
observed in the sample.) Equation 3-10 is plotted in
figure 3-4 for selected values of n.
*For the r th smallest value, P = 2 p \l-
Example:
Data:
n -6
Xi = 850 psi
= 900 psi
= 1050 psi
= 850 psi
= HOG pSi
x 2 = 1100 psi
x 4 = 1000 psi
x 6 = 950 psi
x 3
x 5
X min
Problem: What proportion of the population can
be expected to have resistance levels
in the range from 850 to 1100 psi with
a confidence level of 80 percent?
The solution can be calculated from equation 3-9
with
n =6
a =0.2
Xl 4 = 5.989 (from table 3-2)
or can be found from the curves of figure 3-3.
From either approach it is found that p =57 per-
Figure 3-2. Operating Characteristics Curves for Different
Values of n
TM 5-858-6
LO
CTi
I
^i
CD
.jQ
CD
H
J
1
M
O
CQ
O
CD
4J
PH
cj
O
n
E-
CQ
CO
h- 1
a
x
w
CM
J
to
C4 t>. N ~
000 O -<* N COOO 00
OOO ~ 3-O J>OO
OO 00 COOO CO
rf-00 &O ON rt O O COO O N tOOO
o T N co o co too r^ o co ooo ooo o o
^ ~ to r* rx i/% co o ^oo N ^ m ^^ 1 ~
r"P r^9 9 ^"C ^ ov mvo o <^vo
_ o rf *-> OM
lOOO t-> ^O <
** N ^* io\o oo o o N ro iovo r**oo o ** c$ ^" to > o i
M N M N CiM <S COCOCOCOCOCOCOTj-^f-^-^^-Tj-'
SS P 21 * 5^ ^
oo . ovvo o^
^-0 vo 10 C>
ooo vo
N 000 .-T ^->
noo
co o ix o -< N rj- 100 oo o N co ^o r-oo b ^ N co too f-ob b ^ N r*
MM^ww^^NNMNNNNCOCOCOCOCOCOrOCOTJ-^^^
r^-oo o *- N co -s}- 10 t^-oo o b N co V tr>o r^> o b
r-.^^clNlNNNNNNCOCOCOCOCO.COCOCO^
f> Qx O -
o o N yop p N -<ro oo o i co
> ^<r o i>oo o ^ N co TT ioo cb o b ^ M co too Kob o b N ^ ioo
w^^^^^HH^c<NNNC<<SNMC<COCOCOCOCOCO
O
^f OO
^
ci ro iro r^op N co
t^oo o o N ^-
r^-op op p *- N coco-^fto
r^oo o o >-< N co Vo f^-ob o b ^ N co
- - 1-1 NNCJNNNNNNCOCOCOCO
O N co ^- ovo t^oo o 6 1-1 N co
\ O - N co ^ too rob o
MNNNNNNNNN
OO COTj-
^r^N
rr^T
O O -
CO CO <* lOO f>-00 OO6 ~ Cl CO rj-
-, oo o
?*
r^oo ooo - N co^ftn
MH4^ M (sir^c<ciNM
N
00Nrofo-4- 100 o r-cb o 6 N N co ^- Co
o r^ob ob o 6 ^ N co
&
b
.
^-00 iocoOl-tocoOopO?cT o? o ^ N - 0^.
roTt-rf too t>. i>oo obb^Nco^-^- ioso f^ci) ob o
o
> ^ ^^ co ^ co io co o oo o co - o t
^^MNcoco^-io ^vb r- f-ob obb-NcocoV ^oo o f-ob
*
b
If HH1
too ^. ^o
11 1 ? SI
8 ?
? 2
ioo f> f-cb ob
M N CO ^ 100 t^OO M N CO
r^oo o o -> N co ^ too r*-oo o o
^Mi-.Nf<NNr<f<nf<f1ro
W
O
CJ>
X
co
TM 5-858-6
Figure 3-1. Operating Characteristics Curves for Different Values of n
3
fe
1L
PI
ESS
2g
Q
W
CO
I
o
H
W
H
O
hH
CO
w
w o
w o
hH II
hH
Q C5
U
O
fc
CO
W
>
Pi
D
CJ
CO hH
CJ CO
co o
hH
pq pj
E-" >
CJ PJ
^ <
CJ DH
cjg
5 H
E-H CO
o^ pq
2 H
O -P
H 9Niid30ov jo Aimavaoyd
CJ
3-8
5-858-6
100
90
80
70
60
50
40
30
20
M
CO
LU
_1
o.
10
9
8
7
6
5
k
Figure 3-3. Percentage of Population Within Sample Range as a
Function
P = CONFIDENCE LEVEL
-0.95
0.90
0.80
-0 . 75
0.70
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PROPORTION OF POPULATION INCLUDED IN SAMPLE RANGE, p
1.0
U.S. Army Corps of Engineers
FIGURE 3-3. PERCENTAGE OF POPULATION WITHIN SAMPLE RANGE AS A-
FUNCTION OF SAMPLE SIZE
3-9
TM 5-858-6
cent. Thus, it can be asserted with a confidence of
80 percent that 57 percent at least of the popula-
tion will have resistances falling in the range from
850 psi to 1100 psi. No inferences can be made for
the remaining 43 percent. (Harris, 1952)
/. Inferences using distribution of exceedances
can be made using the same data presented above.
Problem: With a confidence of 80 percent, what
is the maximum proportion of a fu-
ture very large sample which could be
expected to fall below the 850-psi
minimum of the sample of 6 observa-
tions?
The answer can be calculated from equation 3-10
above by solving for p with n =6
P =0.80
Or the curves in figure 3-4 can be used. From
either approach,
p ~ 23.5percent
Thus, no more than 23.5 percent of a large sample
from the population can be expected to have resis-
tances below 850 psi with a confidence of 80 per-
cent.
3-6. Binomial distribution.
a. As stated previously (para. 3-1), the verifica-
tion of whether the resistance of a system is equal
to or greater than a specified hardness level re-
quires a somewhat different approach than deter-
mining the level of the resistance. This approach
uses the statistical inferences of a binomial dis-
tribution.
b. The data that will be used in the analysis will
be "failure-success" type of information: Did the
system, subsystem, or element fail or succeed under
test or in the calculation when subjected to the
specified environment? When performing verifica-
tion testing this does not eliminate the need to
fully instrument the test item to acquire all per-
tinent response data. Comprehensive instrumenta-
tion becomes more important as the specimen and
test costs increase.
c. Verification tests or analyses for this type of
investigation are conducted at a specified hardness
level, usually the design hardness goal. However,
tests or calculations can also be conducted at levels
exceeding the hardness goal. Such a decision is
made by the verification analyst in conjunction
with the designer and system manager. If tests or
calculations are to be performed at levels other
than the design goal, the level must be related to
the design goal through analysis that is performed
separately from the verification analysis presented
in this volume (i.e., a full quantal response analy-
sis).
d. Acquisition of resistance data and the analysis
for determining whether the resistance is at least
the specified hardness level will follow basically
the same sequence of steps as for the resistance
level itself (para. 3-4). The hardness compliance
data will almost always be composed of fewer than
30 samples. However, as previously stated, the sta-
tistical inferences will be made from a binomial
distribution because of the "go/no-go" or
"pass-fail" nature of the data. The basic informa-
tion required for the verification analysis is pro-
vided below.
e. The confidence intervals can be determined for
two conditions:
P(s=r|n,p) =
n!
r!(n-r)!
P r q n
(3-11)
which gives the probability of realizing exactly s=r
successes in n trails (where the probability of suc-
cess for any one trial is p, [q =1 p]; p can take
any value from to 1; 0<p<l. Alternatively,
P(s>r|n,p)
n
n!
s!(n-s)!
p'q"
(3-12)
s=r
which gives the probability of realizing r or more
(s>r) successes in n trials.
/. Both equations 3-11 and 3-12 can be evaluated
directly or tables may be used. Extensive tables are
included in Abramowitz-Stegun (1972), and for val-
ues up to n =10 are included for convenience in
appendix A.
g. Generally, equation 3-12 will be used in the
verification analysis, since the question usually
posed to the verification analyst is: "Is the resis-
tance equal to or greater than r, where r =r/n?",
rather than, "Is the resistance exactly equal to r?"
h. In the population being considered (the total
number of like elements, subsystems, or systems in
the total deployed system), an unknown proportion
3-10
Table 3-2. The a? Distribution
TM 5-858-6
0) .
Q
W
Q
hH
CO
I
PJ
O
PL,
PL,
O
CO
PJ
nJ
>
PJ O
PJ O
HM
PL, II
HH
Q 5
O W
P^ O
CO
W CJ
> HH
P< PU
^D HH
U Z
U
CO M
O CO
CO O
PJ PJ
CJ PJ
3 <
O
E- CO
<v pi
PJ
O -P
CN
I
H 9Nlld333V JO
3-n
TM 5-858-6
Figure 3-4. Percentage as a Function of Sample Size and Probability
10 20 30
PERCENT, p
(Proportion of population falling below minimum sample value)
3-12
TM 5-858-6
: items will withstand the imposed environment
lesign goal environment). This proportion will al-
ays remain unknown unless the entire population
. tested. However, this unknown proportion (p)
in be bounded by confidence limits for a specified
mfidence coefficient (P) (e.g., 90 percent such that
f <p <p^or p >p^in which p^and p^are the lower
ad 90 upper bounds, respectively.
i. The discussion in paragraphs 3-4 e and / re-
irding a and /3 are also applicable to binomial
istributions. The basic approach (Mace, 1964) is
immarized below.
j. The hypothesis to be tested is H,,: p >p , where
is the true but unknown proportion of successes
L the population and p is the least favorable value
lat is acceptable. As before, a is the probability
' rejecting H^ when actually it is true, and j8 is
le probability of accepting p>:p when actually p
:p b where p x <p
et: n = Number of tests in sample
s = Number of successful tests
Then
Accept H : p >:p if s >:h +nm.
Reject H : p >:p if s <h x +nm.
Conduct an additional test if
hi -fnm =<s <h =nm
Example:
Problem: Test the hypothesis: H :p <(p =0.90)
for a =0.10.
Let p!=0.70 and /3 =0.30
(Note: /3 =0.30 implies that there is not much
concern about accepting p>0.90 when actually p
=0.70. If there is concern, choose <0.05.)
Data:
n =5
s =4
0.1
0.3
m =
efine:
m =
1-Po
1-Pi
PI
-
PC
1-Po
-
1-Pi
(3-13)
1- a
IL + 1 "" p
PC + 1-Pl
(3-14)
I- ft
(3-15)
-1.0986
-1.0986
-0.2513+(-1.0986) -1.3497
=0.814
-1.3499
, 0.7
0.1
-1.0986
-1.3499
=0.814
- 1.9459 _ _ 1442
1.3499 -1.3499
-1.442 +(5 x 0.814) =2.628
hi +nm
h +nm =0.814 +(5 x 0.814)
2.68 <s =4 <4.884
4.884
The data show that h x =nm <s h +nm. There-
fore, an additional test must be conducted to verify
the hypothesis at the and ]8 probabilities se-
lected.
For n =9
s =8
h +nm =0.814 +(9 x 0.814) =8.140
s <h +nm
s <hi H-nm
For n =10
s =9
h +nm =0.814 +(10 x 0.814) =8.954
s<h +nm
Accept H :p>:0.90
Thus it would take 10 tests with 9 successes to be
3-13
TM 5-858-6
able to assert that p >0.90, with a confidence of 90
percent, that the hypothesis will be accepted when
it is true, and with a probability of 0.3 of accepting
the hypothesis when actually p could be as low as
0.70.
k. Figure 3-5 shows plots of the functions (h x /n)
+m and (h /n) +m for values of n for p =0.90,
<* =0.10, and j8 =0.25. The curves are developed
from equations 3-10 and through 3-14 and can be
used as follows.
L Select a value of p a that is desired for the
analysis and calculate pj/po. From the (h /n) +m
set of curves, find the value of s/n required for
acceptance of H :p>p for the desired n. From the
(hx/n) +m set, find the value of s/n that would
require rejection of H for the desired n.
Example:
Let Pi=0.70
Pl /p =0.78 (P =0.90)
Accept H :p >:0.90 Reject H :p >0.90
when when
n s/n> n s/n<
10 0.91 (10 10)
7 0.94 (7/7)
5 1.00 (5/5)
4 1.05-
3 1.12-
10 0.66(6/10)
7 0.60(4/7)
5 0.52 (2/5)
4 0.44(1/4)
3 0.32(0/3)
The above data show the following:
For PO =0.90, px =0.70, =0.10 and ft
=0.25, it is impossible to verify the
hypothesis with fewer than 5 tests, i.e.,
it is impossible to have s>n.
For a sample of 5, all tests must be successful
to accept H :p>:0.90
As tests are conducted, the criteria for
rejection can be constantly monitored;
for example, if after 4 tests, 3 have
failed (s =1, s/n =%), the hypothesis
must be rejected for the parameters
selected above.
Problem: What is the proportion (p) of systems
that will survive the design-goal test
environment with an associated con-
fidence coefficient of 90 percent? Thus
we must find p such that p >:P with
a confidence of 90 percent.
Data: n =3 (tests conducted at the design-
goal level)
r =2 (minimum number of successful
tests)
From table A-2, column (n =3, r =2), find the
value nearest to 0.10 (0.10 =1.0 - 0.90). The value is
0.104. In the p column read the corresponding
value, which is 0.20. (Note: the table values can be
interpolated if desired to get the value of p for
exactly 0.10.) This value (0.20) is p . The confidence
interval is p >0.20 with an associated e confidence
coefficient of 0.90. The statement can now be made
(based on the test data) that the proportion of
successes to be expected in the population is
greater than or equal to 0.20 and there is a 90
percent confidence that this is true.
m. When the system manager assumes a priori,
what constitutes an acceptable confidence interval
and when the computed interval seems too low, two
alternatives exist: Conduct more tests with the ex-
pectation that some of those tests will be success-
ful, or decrease the expectation of the confidence
limit and accept the greater risk. For example, if
two or more tests are conducted and both are
successful, then
n =5
r =4
From table A-2, the 90 percent confidence limit is:
p>0.42
If no additional tests could be conducted, a lesser
confidence must be accepted to decrease the inter-
val or increase p. For
n =3
r =2
and a 70 percent confidence, the confidence limit is:
p>0.37
For 50 percent confidence, the confidence limit is:
p>0.50
The results of this example support the observa-
tions of the previous section, i.e., it is impossible to
make high confidence statements with a meaning-
fully narrow confidence interval without conducting
a significant number of tests (even if all tests are
successful). This is further demonstrated by the
curves in figure 3-6.
3-14
TM 5-858-t
Figure 3-5 Determination of Minimum Sample Size
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1-1. Introduction.
a. In verifying whether systems will survive a
>ostulated nuclear attack, both experimental and
Analytic (mathematical) methods may be required.
?he selection of the methods to be implemented is
he responsibility of the systems manager and the
r erification analyst. The decision is based on sys-
em design and mission requirements as well as on:
Accuracy of mathematical models
Cost of calculations
Accuracy of experimental simulation of
environments
Cost of experiment
Number of items available for analysis
6. Although protective and protected systems
nust be capable of withstanding the 13 weapon
jffects described in TM 5-858-2. each system will be
nore susceptible to some effects than to others. If
:he facility and its contents are resistant to par-
:icular effects, the system is defined as super-hard
tfith regard to those effects, and verification will
lot be required. Conversely, some systems may be
/ery susceptible to some effects, and redesign
rather than verification is required. It is primarily
:oward those systems whose survivability is mar-
ginal that the verification program is directed.
c. Verification studies must consider the free-
field weapon-effect load, the local load at the sys-
tem, subsystem, or element level via the transmis-
sion path between the free field and the local load
point, and the resistance of the system in question.
System managers must define the free-field
weapon-effect load, the transmission path charac-
teristics, and the system resistance probabilistical-
ly, i.e., in terms of their mean values and their
coefficients of variation (COV's). In general, a de-
terministic assessment of hardness will not be ac-
ceptable.
4-2. Simulation requirements.
a. Definition of the local environments that ex-
cite systems, subsystems, and elements is a signifi-
cant effort that must be accomplished to provide
input to the verification analysis. Although it may
not always be the case, the verification analysts
likely will inherit responsibility for defining local
loads, since they have access to the data from
which input loads would be derived and they are in
the best position to understand the true nature of
those environments.
6. The transmission of the primary weapon-effect
loads from the free field to the input points of the
systems is highly dependent on the threat (weapon
size and number, height or depth of burst), the
siting conditions (geology), and the configuration of
the facility. The general characteristic of the free-
field nuclear weapon effects are presented in TM
5-858-2. Although it is not practical to present a
comprehensive discussion of the methods for simu-
lating the transmission of the particular weapon
effect from the burst point to the hardened target,
a recommended methodology is presented in chap-
ter 6.
c. The system/weapon-effect combinations of
protective system for which hardness assessment
must be accomplished are presented in table 4-1. It
must be recognized that each of these systems will
contain numerous subsystems and elements. In
many instances it will be necessary to perform the
verification analysis at the element or subsystem
level. For each separate item to be analyzed, spe-
cific requirements and methods will need to be
defined. Simulation requirements and techniques
must be fully developed, evolving finally into a
comprehensive test and analysis plan to guide the
conduct of the analysis.
<L Protected systems must also be subjected to
hardness verification. These systems are not sepa-
rately addressed in this manual. However, in most
cases they must be hardened only to the local
environment within the protective structure or on
the shock-isolation system.
e. Experimental techniques are used to generate
input that simulates the overpressure, ground
shock, and EMP nuclear weapon effects for ver-
ification analyses. Exclusion here of techniques for
the other effects presented in TM 5-858-2 does not
imply that these effects can be ignored. The sus-
ceptibility of each subsystem to all effects must be
determined and verification testing conducted if
necessary. However, in general the subsystem de-
sign(s) will be governed by these three weapon
effects. The GE-TEMPO (1972) and Bednar (1968)
reports present detailed information for some of
the techniques that were in use in 1972 and 1967,
respectively. Excerpts from both are presented in
appendix B.
4-1
IM 5-858-6
Table 4-1 Protective Systems: Requirements for Weapon-Effect
Hardness verification
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TM 5-858-6
-3. Simulating and testing
trerpressure.
Design. The airblast environments will have ex-
erne variations. Surface/flush structures/ systems
the surface elements of air-entrainment systems
ay be designed to survive peak overpressures of
'00 psi and greater, whereas aboveground facili-
3s may only be required to survive tens of psi or
3S. No single technique or tool is adequate to
oviding the simulation-testing capabilities
quired for verification throughout this range.
(1) Because large field tests usually are pro-
ded by a central agency, involve numerous other
^encies, and may be available only once during
ie total verification process for a particular fa-
lity, the opportunity should be optimized. This
eans that the resistance of all critical elements of
ie system or subsystem to be tested must be
stimated beforehand with corresponding
icertainties. Furthermore, the incorporation of
tese resistances into a complete system, as de-
:ribed in chapter 6, must show a high probability
lat the system will survive. The system is then
elded such that the design environments are sim-
.ated as closely as possible. Replication of the
isted system at different ranges from ground zero
very desirable in order to acquire data above and
slow the design environment.
(2) It is most important that the actual local
>ad inputs and the failure-mode responses be ac-
irately measured to provide results of high statis-
cal confidence that will credibly support a final
DSt-test verification statement. Depending on the
Bgree of simulation achieved for the environments
f interest, it may be necessary (as discussed
bove) to base the final verification statement on a
ilculation from a verified mathematical model.
b. High-exp^sive simulation technique (REST)
ists. The basic configuration of a HEST test is
lustrated in figure 4-1. A cavity is constructed
ver the test item. The amplitude of the peak over-
ressure is controlled by the density of explosives,
enerally Primacord, in the cavity. The positive-
hase duration is governed by the depth of the
iircharge, and the propagation velocity is governed
y the wrap angle of the Primacord.
(1) Combustion products of the Primacord are
eleased at a rate that is proportional to the
'rimacord wrap angle. These products act as a
iston to drive a shock wave into the undisturbed
avity volume. As the generated pressure acts
.gainst the overburden, the cavity volume increases
,s the overburden rises, causing the prssure am-
plitude in the cavity to decay. It is this process
that produces the fast rise and exponential decay
to simulate the nuclear overpressure.
(2) A HEST test can be configured to produce
a blast wave that provides, for short durations,
good simulation of the overpressure from weapons
that extend up to the megaton range. Because of
the limited duration that can be simulated, stress
attenuates in the ground more rapidly with depth
than for the nuclear event and the displacements
will be smaller. Hence, the early dynamic responses
of the tested system will approach those that
would be induced by the nuclear event, and good
simulation of peak accelerations and velocities is
achieved; but late-time rigid body motions are not
well simulated.
(3) The technique is applicable primarily for
testing surface-flush and shallow-buried structures
where the principal failure mode considered is di-
rectly related to overpressure loading. Dynamic
pressure effects are not well simulated by the
HEST test, and failure modes related to this effect
must be tested separately. Because the peak over-
pressure is essentially the same over the entire test
area, specimens of large dimensions can be realisti-
cally loaded in a HEST test. Both full-scale and
model structures can be tested in the HEST test
bed.
(4) Even though the positive-phase duration
does not simulate the nuclear event at late times,
the duration is usually sufficient to provide ade-
quate loads for direct verification when the over-
pressure impinges directly on the test item. Thus,
good verification data can be obtained for most
deformational failure modes for surface-flush sys-
tems such as structures and closures. Further in-
formation on HEST is available in D'Arcy et al.
(1965), D'Arcy-Clark (1966), GE-TEMPO (1972),
and ble Traindafilidis-Zwoyer (1968).
c. High explosive (HE) field tests. Many HE tests
have been conducted to provide overpressure and
ground-motion environments in sizes varying from
a few hundred pounds to hundreds of tons of equiv-
alent TNT. For overpressure studies the explosives
are placed in spherical or hemispherical arrange-
ments at or above the -earth surface, typically as
shown in figure 4-2.
(1) The blast wave produced in an HE test
provides good simulation of the peak amplitude for
both the overpressure and dynamic pressure. The
peak pressure amplitudes from an HE burst decay
more rapidly with distance from the center of the
charge than do nuclear bursts because usually less
weapon yield is available. Because of this, only the
4-3
TM 5-858-6
Figure 4-1. Sketch of HEST Facility
4-4
TM 5-858-6
-ger tests (e.g., 500 tons) are adequate for testing
ll-scale elements. For large systems, the system-
;e/peak-pressure combination of interest will
nerally dictate that testing be performed on
)dels of subsystems. Certain elements such as
sures and blast valves may be subjected to good
nulation of peak loads for direct verification.
(2) HE tests provide an airblast environment
at is comparable" to the nuclear environment es-
cially at peak overpressures below 300 psi. Good
nulation of overpressure is provided for a wide
age of yields but particular attention must be
-ected to proper scaling. The yield dependence is
^cussed in chapter 7 of TM-5-858-2. Further fo-
rmation on HE tests is available in Kingery
)68) and in Reisler et al. (1975).
d. Airblast simulators. In addition to the large-
ale field tests described above, there are fixed
^ilities designed to produce blast waves that sim-
ate to some degree the blast wave from a nuclear
ent. Many of these facilities are listed in appen-
< B and are useful for component or element
sting. Two of the larger facilities of this type are
ABS and LBLG, described below.
e. Giant reusable airblast simulators (GRABS).
te GRABS facility is located at the Kirkland AFB
d is operated by the Air Force Weapons Labora-
ry (AFWL). The basic configuration of the
rlABS facility is shown in figure 4-3. The facility
ovides for a soil depth of up to 30 feet for
iplacement of the specimen to be tested. The
lount of explosives, cavity volume, and soil sur-
arge depth are selected to produce the pulse de-
-ed within the range of the facility capabilities.
le mechanism of producing the pulse is similar to
at of the HEST test except that the pressure
Ise does not horizontally traverse the specimen
.t loads are areas of the test bed simultaneously
.d essentially equally. Simulation of the peak
erpressure history is similar to that achieved in
HEST test. The size of the facility allows for
sting of full-scale elements; subsystems and sys-
ms would generally be modeled for testing. The
st s design must consider the reflecting bound-
ies of the facility. The s response time(s) of the
ilure mode being studied must be such that the
itical parameters have reached peak amplitudes
fore reflected waves reach the location of inter-
t. Further information on GRABS is available in
irtel and Jackson (1973) and Jackson et al. (1973).
f. Large blast load generator (LBLG). A number
blast load generators listed in appendix B and
scussed by GE-TEMPO (1972) and Bednar (1968),
varying sizes and designs have been used to
conduct verification tests on full-scale elements and
models of elements and subsystems. One of the
largest of such facilities is the Large Blast Load
Generator (LBLG) located at the U.S. Army En-
gineer Waterways Experiment Station (WES). The
basic configuration of the LBLG is shown in figure
4-4. Further information on LBLGs is available in
Albritton (1965) and in Kennedy et al (1966).
(1) A soil bed of up to 10 ft deep can be loaded
for emplacement of specimens to simulate buried
conditions. Peak pressure and positive phase dura-
tions can be controlled within the range of the
facility capabilities. Durations equal to or exceed-
ing those from megaton nuclear events can be
achieved.
(2) Airblast loads for elements and subsystem
models can be provided to accurately simulate nu-
clear effects. As with the GRABS facility, the test
must be designed such that reflections from the
facility boundaries will not affect the failure mode
response being studied until maximum amplitudes
have been reached.
g. Shock tubes. A number of shock-tube facilities
are listed in appendix B and discussed by GE-
TEMPO (1972) and Bednar (1968). In general, such
facilities provide a good simulation of the airblast
characteristics of a nuclear event, namely peak
overpressure, decay rate, positive-phase duration,
and dynamic pressure. Shock tubes are used for
testing subsystem models and small full-scale sys-
tem elements. However, depending on the response
of the failure mode being studied, verification can
be accomplished through scaling. Direct full-scale
verification testing of the performance of air-
breathing equipment can also be accomplished in
shock tubes. Shock tubes have also been used to
perform debris-impact tests. Further information
on shock tubes is available in Lane (1971).
4-4. Simulating and testing ground
shock.
a. Overpressure-induced and crater-induced. The
techniques and facilities that are used to simulate
the ground-shock environment from a nuclear
event are the same whether the shock is induced
from the overpressure or the crater formation. The
environments, motion and stress, created by the
two sources are very different as presented in TM
5-858-2, and are dependent on combinations of
weapon nt size, height or depth of burst, and sur-
rounding media. Some of the tests t described
above for simulation of overpressure are also used
for ground shock. It is generally the objective, par-
ticularly when testing full-scale subsystems or ele-
ments, to simulate the airblast and ground shock
4-5
TM 5-858-6
Figure 4-3. The Giant Reusable Airblast Simulator (GRABS)
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4-6
Figure 4-2. Typical HE Field Test Configuration (Spherical
Charge)
TM 5-858-
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Figure 4-4- Large Blast Load Generator (LBLG)
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4-8
TM 5-858-6
s iltaneously. Only in rare circumstances is this
a .ally accomplished. Usually one environment or
t other must be compromised. Whether over-
p ,sure or ground shock is most important is a
d sion that must be made by the verification
a yst. The decision is based on the susceptibilit
o lie failure mode(s) being studied to the particu-
1; design environments. Many times, separate
t< 3 will be required to achieve complete verifica-
t: of the system.
HEST test. The HEST test described above for
s ilation of overpressure is one of the best tech-
n tes for studying overpressure-induced vertical
g ind motion over relatively large areas. How-
e , as with all simulation techniques, a com-
p 3ly satisfactory simulation cannot be achieved.
(1) Because of the complex geometry of the
t< facility and the relatively small surface on
v ih the pressure load acts, the ground motions
t. occur in a HEST test probably are more com-
p than comparable responses in a nuclear envi-
r nent. The HEST test does not simulate all as-
p s of nuclear ground shock; because of the finite
d ensions of the test cavity "edge effects" distort
i. measured response.
(2) Analyses performed for HEST programs
i] eate that, in some regions beneath the test bed,
p c vertical and horizontal-longitudinal (in the
d ction of the blast-wave propagation) accelera-
t s, velocities, and stresses are reached before
e j-induced (relief wave) responses can influence
pressure-induced responses. Figure 4-5 shows
i. e regions. The analyses also show that the peak
d lacements, which occur late in time and include
e j effects, do not simulate nuclear responses.
C er responses, such as the horizontal-transverse
(; pendicular to the direction of the blast-wave
p )agation) and beneath-berm motions, are also
I- 5T-unique and have no direct relationship with
t nuclear problem.
High explosive (HE) field tests. HE field tests
d gned to simulate overpressure also produce
g ind shock. However, the limited yield of the HE
d ce usually precludes testing of items other than
e lents or models. Moreover, ground motion is
c Really dependent on the geology, so it is difficult
t )cate an HE test site that scales geologically to
a >perational site.
(1) The predominance of one motion over the
c >r (overpressure-induced and crater-induced) de-
li is on the different attenuation rates and con-
s lently on ihe Distance from ground zero where
r ion is measured, and on the particular motion
1 imeter considered and the associated direction.
Overpressure may dominate the acceleration at all
ranges of interest to this volume except deep-based
systems. However, the crater-induced accelerations
may cause larger maximum displacements. In gen-
eral, overpressure-induced motions will contain
higher frequency components than the crater-
induced motions, especially near the ground sur-
face.
(2) The familiar HE test configuration shown
in figure 4-2 is not effective in simulating the
crater-induced ground-motion weapon effects. To
circumvent this, special configurations of charge
burial are used as shown in figure 4-6. Using finite
element computer codes, the configuration of the
charge is calculated for the particular geology,
yield, and HOB/DOB combination of the nuclear
weapon to be simulated. This technique produces
good simulation of the crater-induced motions but
does not simulate the overpressure. At this time
(1976), accurate verification of both effects cannot
be achieved in a single test event. Further informa-
tion on HE tests is available in GE-TEMPO (1967,
1970, 1973), Stubbs et al. (1974), and Rooke et al.
(1974 and 1976).
d. HEST-BLEST. The HEST test is limited in
effectiveness by the size of the test bed/cavity; the
HEST-BLEST concept shown in figure 4-7 was de-
veloped to overcome this deficiency. Here, the
HEST cavity is constructed over a relatively small
area where it is necessary to produce the overpres-
sure directly on the surface of the structure sys-
tem. Separate shallow-buried, high-explosive
charges are then placed in a much larger surround-
ing area. This technique of loading the area is
called a Berm Loaded Explosive Simulation Tech-
nique (BLEST).
(1) The BLEST charge array is designed to
simulate the stress environment in the upper sur-
face of the test area that would result from nuclear
overpressure loading. This loading combined with
the direct air-bias from the HEST cavity simulated
the overpressure from a nuclear s event over a
much larger area and for much larger times than
in a simple HEST test. The peak displacements are
not influenced by the unloading waves from the
edge of the HEST cavity.
(2) This test does not simulate crater-induced
ground shock. Further information on HEST-
BLEST is available in Schrader et al. (1976).
e. HEST-DIHEST. As evidenced by the above
discussions on HEST and HE tests, there is no
single technique that produces a totally satisfac-
tory simulation of both the overpressure-induced
ground shock and the crater-induced ground shock
4-9
TM 5-858-6
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'/?v! ^rtw. atid Acceleration can be Attained Without Edge
Interference.
DISTANCE ALONG TEST BED (LONGITUDINAL OR TRANSVERSE), FT
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4-10
TM 5-858-6
Figure 4-6. HE Test Configuration to Simulate Crater-Induced
Ground Shock
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TJVt 5-858-6
Figure 4-7. HEST/BLEST T Configuration
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4-12
TM 5-858-6
effects. Therfore, tests have been designed that
combine the HEST test with DIHEST
(Direct-Induced High-explosive Simulation
Technique) to produce both effects simultaneously.
(1) The basic configuration of a typical HEST-
DIHEST test is shown in figure 4-8. This test is
designed to combine overpressure and limited
ground shock from the HEST test with crater-
induced ground shock from the DIHEST test. The
DIHEST test uses a buried array, usually planar,
of high explosives that are detonated
simultaneously, to produce a predominately hori-
zontal shock wave on a test system. Timing of the
detonation of HEST and DIHEST explosives sys-
tems and location of the DIHEST array require
extensive pretest experiments and calculations.
(2) Tests have been conducted in both rock and
soil media. The size of the HEST cavity, as well as
the design of the DIHEST array, influences the
duration over which the ground motion is simu-
lated. Generally acceptable simulation of accelera-
tion, velocity, and stress peak amplitudes are ac-
heived.
(3) Further information on HEST-DIHEST is
available in Schlater (1972) and Blouin (1969).
/ Mechanical tests. The tests discussed for the
simulation of overpressure and ground shock apply
to scale model and full-scale testing of systems and
subsystems. However, before field or large-scale
laboratory tests are conducted, and before a system
has been fabricated, comprehensive testing will be
performed on elements and small subsystems.
These tests, conducted to obtain data for basic
development and verification, are mechanical tests,
in which the excitation force is applied directly to
the specimen through a known mechanical connec-
tion.
(1) Mechanical tests are generally the simplest
and least expensive to conduct; the specimens are
relatively small (i.e., measured in feet rather than
tens or hundreds of feet), and the test equipment is
readily available. Because of these factors, this
type of testing is popular, and most of the statisti-
cal data to determine the mean resistance and
uncertainty associated with a particular failure
mode will be acquired with these tests.
(2) The greatest limitation of the mechanical
test is that it is not directly comparable to the
free-field weapon-effect ground shock. Therefore, it
is necessary that supporting analyses and tests
(often very complex and costly) be conducted to
translate the free-field ground shock to the local
input environment. Nevertheless, compared to the
unwieldy field test and the large-scale laboratory
test, the mechanical test will generally be the most
used tool in the verification process.
(3) There are numerous techniques and facili-
ties used to conduct mechanical tests. A discussion
of some of the most applicable facilities is pre-
sented in appendix B and in GE-TEMPO (1972) and
Bednar (1968). However, in many instances it will
be necessary to apply basic force-producing equip-
ment such as shakers or rams, in a manner that is
unique to the element-input requirement combina-
tion being addressed, and no existing fixed facility
would be adequate.
(4) In many instances it will be required to
perform a verification test of a large subsystem in
a full-scale operational mode (e.g., of critical con-
trol and communication equipment supported on a
shock-isolated floor or platform). In such cases,
where fixed-facility tests are prohibitively costly,
pulse-train simulation tests have been conducted
for verification. This technique applies specifically
designed force-pulse trains at the required number
of locations, directly on the platform structure,
such that the platform response simulates the re-
sponse experienced by the total shock-isolated sys-
tem as a result of the motion induced in the pro-
tective structure by the ground shock. The tech-
nique uses measurements of impedence and transfe
functions on the as-built, in-place subsystem to
transfer the motion from the attachment point of
the protective structure to critical locations on the
platform. With the equipment elements in place,
these motions are then simulated on the platform
by application of the force-pulse trains.
(5) Further information on mechanical tests is
available in Safford and Walker (1975a and b).
4-5. Simulating and testing EMP.
a. Uniqueness. The waveform and corresponding
frequency spectrum for a nuclear EMP differ sig-
nificantly from other man-made electromagnetic
disturbances or from natural phenomena such as
lightning. The pulse rises very rapidly
(nanoseconds) to the maximum level (hundreds of
kilovolts per meter for the electric field) and then
decays exponentially. The frequency range is exten-
sive, varying from UHF to VLF. Also, the EMP
field is widely distributed, whereas g lightning is
localized. Because of these characteristics and dif-
ferences, designing to protect against EMP or to
simulate for verifying hardness requires EMP-
unique approaches. The verification of EMP hard-
ness will us both analysis and testing techniques.
4-13
TM 5-858-6
Figure J>-8. Typical HEST/DIHEST Test Array.
<D
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TM 5-858-6
6. Verification analysis. The analysis techniques
presently available are sophisticated enough to
identify areas of weakness in the system design, to
guide test selection/design, and to confirm the ac-
curacy of test data. However, specific points of
weakness and specific quantitative levels of hard-
ness cannot be calculated.
c. Experimental analysis. The analysis of the
system can be accomplished using computer codes
that model the many elements of the system. An
experimental analysis can also be performed that
consists primarily of measuring the impendance
and transfer functions between critical system
junctions and then involving these functions in
time, or multiplying them in the frequency domain
with the postulated threat environment inputs. The
predicted total response will be very accurate as
long as the responses of all elements in the mea-
sured path remain in the linear range.
d. Verification testing. Both laboratory and field
tests are conducted to provide the required simula-
tion for hardness assessment. Hardness evaluation
for EMP may also use scale-model and component
testing; however, these tests are generally not used
for final verification analysis. In general, all sys-
tem components will be separately tested in the
laboratory prior to being included in a system or
subsystem test, the test data being integrated.
Testing is used to verify calculations to confirm
general hardness of the design and identify specific
weaknesses, and to provide bounds for final ver-
ification testing.
c. Subthreat-level testing. Subthreat-level tests
performed on elements or on systems to define the
manner in which the EMP field couples to the test
item and to expose weaknesses that were not dis-
covered in the analysis. Techniques used for
subthreat-level testing are the following:
(1) Low-level transient: The threat time his-
tory is simulated but the amplitudes are below the
threat level.
(2) Repetitive pulse: A train of pulses (10 to
100 per second) is applied. The threat time history
may not be simulated, but the frequency range
must be the same as that of the threat pulse.
(3) Continuous wave (CW): A continuous wave
is applied to the system. The wave may be swept
across a broad frequency range or applied at dis-
crete frequency steps.
(4) Direct injection: Any of the above signals
can be directly applied at one or more parts of the
systems.
(5) Stationary field: Small items are subjected
to field-coupling tests.
/ Threat level. Threat-level testing requires that
the simulation of the threat be applied over a
volume that is large relative to the total system
being analyzed. When this is accomplished, the
hardness (or lack of hardness) is verified by ob-
serving selected critical system responses. Since the
verification is accomplished through observation of
system responses, the threat-level test environment
must accurately simulate at least the following:
Propagation direction of both the electric
and the magnetic fields
The pulse shape and frequency spectra of
both fields
Peak amplitudes greater than the threat
magnitude
Relative magnitudes of electric and magnetic
fields
(1) The above requirements must be satisfied
for each threat scenario for which hardness is to
be verified, and the electric and magnetic fields
must be developed over a volume larger than the
volume of the system to be tested. The arrival
direction and polarization must be addressed if
total hardness is to be verified. It is also necessary
that the on-line operation of the system be ac-
curately defined such that the simulation can be
imposed at the time(s) of maximum susceptibility.
(2) High-level transient field tests are required
for total threat-level testing. However, some degree
of verification can be accomplished at threat level
using direct injection.
g. Simulation facilities. There are numerous fa-
cilities that have been developed to provide EMP
simulation for various systems and components.
Many of these facilities are listed in appendix B. A
comprehensive treatment of EMP design and ver-
ification can be found in COE (1974) IITRI (1973),
Whitson (1973), and Schlegel, et al. (1972).
4-15
5
5-1. Introduction
a. The analytical approach is an important and
well-established tool to support hardness verifica-
tion. In situations where a physical system does
not yet exist or, if it does, cannot be tested, the
analytical approach may be the only way to assess
hardness, survivability, vulnerability, etc. Unlike
experimental verification which naturally lends it-
self to a statistical presentation, computational
verification almost always depends on deterministic
tools to provide system response to nuclear weapon
effects. These deterministic tools generally produce
sophisticated information of the most probable re-
sponse of the system (the mean), but quantifying
uncertainty will involve a laborious selection of
values for the random nature of system param-
eters.
b. Although the design load for a system, sub-
system, or element will sometimes be the input for
verification analyses or tests, it may also occur
that updated information will be available to better
define the local load environment. Thus, the ver-
ification analyst may not only be responsible for
assessing the survivability of the system to its
design loads, but he may also be required to re-
assess the local design load to reflect more realistic
conditions. Part of the reassessment will come
about as a natural consequence of verification stud-
ies because the response of one system may be the
load to another. Verification of the first system
may indicate that the load to subsidiary system is
different than expected. If the verification analyst
is also charged with the responsibility for deter-
mining system survivability, he must be prepared
to view the verification study from a system en-
gineering point of view, since he will be the one
most likely to intelligently assess the adequacy of
previously established design criteria.
5-2. Computing uncertainties and
survivability.
a. Uncertainties.The total coefficient of variation
of a random variable X, designated by fl x is ob-
tained from
(5-1)
Here, 5 X models the natural randomness of X,
whereas A x represents the uncertainty arising from
errors in estimation. If X itself is a function of
several random variables,
then using first-order linear approximations
(Ang-Cornell, 1974)
(5-3)
and
Q$=Q|
N
n=l'
N N
where
f = Total coefficient of variation associated
with the functional form of X
= Total coefficient of variation associated
n with Y n
Correlation coefficient of Y n and
X =f(Y 1 ,Y 2 ,Y 3 ,...,Y n ,...,Y N )
(5-2)
The subscript V denotes that <5f/SY n is to be
evaluated at the mean values of the variables. Im-
plicit in equations 5-3 and 5-4 are the assumptions
that fiY n 21 and nonlinearity in f near the
mean values is not large.
b. Survival probability. Consult chapter 9 of TM
5-858-1 for a description of survivability models
and chapter 11 therein for a presentation on sur-
vivability allocation.
5-3. Types of analytic techniques.
a. In performing verification calculations the out-
standing problem stems not from finding a suitable
deterministic model, but rather once having se-
lected a model from interpreting results pro-
babilistically. There have been attempts to produce
compendia of the many analytical techniques that
have been applied to calculating the response of
systems undergoing nuclear attack (AE WES,
1972). There is almost never an obviously "best"
technique to solve a particular problem. The "best"
solution depends on understanding all available
techniques; the time frame and cost constraints;
the accuracy desired, i.e., whether the assessment
is preliminary of final; the relative elegance of
concomitant analyses; and the state of the art.
5-1
TM 5-858-6
b. To be meaningful, verification analyses must
be performed probabilistically, i.e., local loads and
system responses must be expressed in terms of
uncertainties, and system survivability must be ex-
pressed as a probability. Uncertainty is defined as
the standard deviation of the load and response
normalized to the mean. It usually occurs that the
the best estimate of the calculated mean response
is obtained with the most complete (and usually
most expensive) mathematical models. However,
the more complicated the models, the more dif-
ficult it is to estimate variations in the response
due to variations in model parameters.
c. Virtually all analytical methods have been de-
veloped to solve differential equations or to repre-
sent solutions of those equations. For most real
systems, the solution of differential equations is
accomplished via numerical techniques, using dif-
ferencing techniques. Alternatively, the computer is
used to numerically evaluate integral solutions or
closed-form solutions. Volumes TM 5-858-3 and -4,
GE-TEMPO (1974b), and AE WES (1972) reference
computer programs pertaining to various weapon
effects as well as descriptions of the phenomenol-
ogy computer codes that calculate the free-field
loadings, which the verification analyst may find
useful.
d. It is important that the verification analyst
recognize that using more sophisticated computa-
tional tools is equivalent to the reduction of (or the
attempt to reduce) systematic uncertainties. In
other words, these techniques are designed to mini-
mize bias in the results. This reduces the ignorance
factor and the uncertainties. An obvious conse-
quence is the saving of dollars spent avoiding fa-
cility overdesign that otherwise would occur due to
use of poor computational tools. The analyst should
also recognize that bias and random uncertainty
can be reduced by using better data, i.e., more
accurate loads and specifications of material prop-
erties.
e. Another resource available to the analyst are
functional relationships derived from regression
equations applied to experimental or computed
data in which the response of systems is defined in
terms of the important parameters of the system.
These solution techniques often are empirical or
semi-empirical, and are found in various sources,
such as Crawford et al. (1974) and TM 5-585-3. The
verification analyst will find most of this informa-
tion unsuitable for performing deterministic ver-
ification analyses; i.e., for calculating the mean
response. Nevertheless for the probabilistic analy-
ses discussed subsequently, these techniques may
be quite useful.
/. The verification analyst may avail himself of
the following techniques for determining the mean
response of systems that are subject to nuclear
attack:
Explicit solutions of differential equations
Numerical solutions of differential or
integral equations
Semi-empirical relationships developed from
regression analyses applied to
experimental and calculated data
The last technique is most often applied to the
design of systems and the first method is usually
too idealized to be much pratical usefulness; the
second approach offers the greatest potential to
generally address the verification problem.
g. Compared to those methods available for cal-
culating the mean response of a system, estimating
the expected randomness due to natural variations
in material properties and in geometries is grossly
more difficult, a task for which little experience
exists and few tools have been developed. Although
there is awakening of interest in the probabilistic
aspects of system response, most of the current
statistical work is too fundamental to be of much
direct application to hardened-facilities
verifications. Therefore, what is lacking in formal
computational procedures must be compensated for-
with a resourceful application of those analytical
tools that are available.
h. The deterministic methods previously outlined
genrally involve the solution of differential equa-
tions with variable coefficients, whereas deriving
the probabilistic response of systems involves the
solution of those same equations with both variable
and stochastic coefficients. The latter property
sharply limits the methods for calculating the re-
sponse as a random variable. In verification analy-
sis there are, for all practical purposes, only three
fundamental techniques for calculating the randonn
response of systems:
Monte Carlo methods
Engineering judgment
Use of simplified uncertainty analyses
generally involving sensitivity (changes
in response due to changes in system
parameters such as stiffness, strength,
etc.)
The most versatile and reliable of these techniques
is the Monte Carlo method, which can be applied to
almost any problem that can be solved determinis-
tically. However, there are certain negative aspects
to this technique that should be considered (para,
5-4). Due to cost and time constraints or simply
because no better alternative seems to exist, the
5-2
TM 5-858-6
probabilities of the system response may be simply
estimated by applying the judgment of acknowl-
edged experts (para 5-5). On the other hand, if it is
possible to explicitly and functionally express the
relationship between the input and the response of
a system, then direct differentiation of the function
may provide a direct means for calculating uncer-
tainties, and subsequently the survival probabilities
of the systems (para 5-6).
5-4. The Monte Carlo method.
a. The correspondence between the experimental
techniques described elsewhere in this volume and
the mathematica approaches that seek to simulate
the experimental method is achieved by a proce-
dure called "mathematical experimentation." The
form most widely used is called "Monte Carlo" or
the Monte Carlo simulation.
b. A simple application of the Monte Carlo pro-
cess consists of the selection of random variable
from an appropriate probability-density distribu-
tion that describes the loading function and the
geometrical and constitutive parameters of a sys-
tem, and subsequently calculating the deterministic
response for each of the random selections.
c. More complicated applications of the Monte
Carlo technique involve multiple systems interre-
lated to each other. By linking the results of var-
ious Monte Carlo solutions together, verification
analyses of large complex systems can be
performed.
d. Although the Monte Carlo method can be used
in many applications, there are disadvantages that
must be considered: Cost, loss of visibility, and
requirement for statistical input. In order to con-
trol costs, the verification analyst may select a
sophisticated analytical procedure for computing
the mean response of the system (to reduce bias
errors), and select an "equivalent" but simpler
mathematical model for producing Monte Carlo t
solutions (to provide information on the random
nature of the response).
e. In linked analyses, in which the results of the
Monte Carlo problem are used as input to another
Monte Carlo problem, the uncertainties in the final
calculation may be governed by errors in the as-
sumed nature of the randomness of the system
parameters. To minimize costs it is desirable to
reduce the number of Monte Carlo solutions as
much as possible, but the use of a crude Monte
Carlo mesh introduces further uncertainties. These
can be mitigated by increasing the number of solu-
tions, but the improvement in accuracy of the ran-
dom response is relatively insensitive to this tech-
nique.
/. When Monte Carlo calculations are performed,
the phenomenological relationship between the ran-
dom variations in the system parameters and the
random nature of the response may be obscured.
Auxiliary sensitivity studies using simpler models
can help in understanding the parent Monte Carlo
calculations.
g. The Monte Carlo method requires that the
parameters of the system be defined statistically.
These statistical data are obtained experimentally
or are estimated. Errors can be reduced by con-
ducting more extensive tests to determine the true
nature of the system variables.
h. The verification analyst will want to study the
specialized techniques that have been developed for
the practical implementation of the Monte Carlo
method. One such well-known technique is Rowan
(1974).
i. A modified Monte Carlo approach can be
adopted in which the partial derivatives in equa-
tion 5-4 can be numerically obtained by randomly
varying the independent variables Y n in the vicinity
of the mean value to obtain the corresponding vari-
ation in the function f. The rpocedure is a for-
malization of the method discussed in paragraphs
4-2 e and / of TM 5-858-2, and noted in paragraph
5-6 c below.
5-5. Engineering judgment.
a. In many cases, especially during the early
phases of hardness verification, it will be judged
not feasible to embark on a Monte Carlo approach
or to use the approach discussed in paragraph 5-6.
It may be necessary to estimate the probabilistic
nature of the system response whose mean value
was obtained by deterministic computations. Be-
cause of his or her familiarity with the solution
technique and a grasp of the range of system pa-
rameter variations, the analyst will often estimate
the distribution of responses around the mean
value. This estimate will draw almost exclusively
on experience, coupled perhaps with auxiliary cal-
culations that provided insight into the sensitivity
of the parametrs in the analysis. When using this
method, the analyst should avoid selecting the
most adverse condition of each parameter to assess
the severest system response. The probability of
uniformly encountering the most detrimental ex-
tremes of each parameter is very remote and cor-
responds to a very small probability of
5-3
TM 5-858-6
occurrence much less than the probabilities of
each independent parameter selection.
5-6. Direct of functions.
a. When the solutions to differential equations
can be expressed in a functional form, then the
uncertainties can be calculated by evaluating the
partial derivatives in equation 5-4. For example,
the atmospheric transmission of thermal energy is
often expressed in the simple equation
6. As a pratical matter, the simplified relation-
ships in the response equations may not yield the
best prediction of the mean response, since other
important variables may be overlooked or not com-
pletely represented. Most such simple relationships
are probably more useful for estimating
uncertainty than for calculating the mean response.
It would be more appropriate to calculate the mean
response by using one of the more complete deter-
ministic procedures referenced in paragraph 5-2.
where is a coefficient and R s is the slant range.
The total uncertainty will then be
where fi f is the total uncertainty of the functional
form of equation 5-5, and l a and fl Rs are the total
uncertainties of cr and R s respectively.
c. For systems that are not grossly nonlinear,
equation 5-4 may be solved numberically by vary-
ing the parameters of the system in small incre-
ments to evaluate the various partial derivatives,
df/dXj. Usually, each independent parameter
would be varied at least once above and once below
its mean value so that the derivatives could be
computed from polynomials fitted to the response
calculations.
5-4
6
6-1. Introduction*
a. In order to perform a verification analysis, the
analyst must define the extent of the system to
which the verification procedures will be applied.
The "system" to be verified may be a complete
facility or a functional unit that forms part of the
facility, or a submit, subsystem, or element.
b. Most facilities are so complex that it is neither
practical nor desirable to consider independently
all elements or even all subsystems or systems in a
verification analysis. Usually, many parts of a fa-
cility will not be susceptible to every nuclear
weapon effect or, occasionally, some parts will not
be susceptible to any nuclear weapon effect. Thus,
it is necessary to select (based on estimate of de-
sign loads and resistances) which parts of the com-
plete facility are susceptible and, of these, which
are most prone to failure under a specified attack.
Those parts that are neither susceptible nor threat-
ened will not need further analysis. The remaining
parts will then be subjected to a verification analy-
sis as subsequently described.
6-2. Diagrams, network logic, fault
trees, and Boolean algebra.
a. Procedure. Applying the various techniques
described in previous sections of the manual is
facilitated by following this procedure:
Construct functional block diagrams
Construct network logic or fault-tree diagrams
Write and simplify Boolean equations
Determine resistances and compute element
uncertainties
Define loads and uncertainties
Compute subsystem and system uncertainties
and compute survival probabilities where
required.
b. Functional block diagram. The functional block
diagram is prepared to orient the analyst to the
interrelationships between the physical or
functional parts of a system. It is most commonly
exemplified by schematic diagrams, which are then
used to construct logic diagrams.
c. Network logic and fault-tree diagrams. Net-
work and tree diagrams, both of which can be
useful in hardness-verification programs, are de-
picted in figure 6-1. However, for complete facili-
ties, systems, subsystems, and even elements, the
tree diagram is most often used, since there is
usually no complicated logic that would require
network diagrams. Only tree analyses are discussed
in this volume.
cL Fault tree. An example of a generalized fault
tree is shown in figure 6-2. It is diagrammatic
representation of the interrelationships between
the various failure modes of a system and the
environments that potentially could induce failure.
Generally, it can be said that a fault tree for a
complete facility consists of N systems, each of
which has M subsystems, each of which is in turn
composed of Q elements. An element will have z
functional failure modes, each of which is excited
by S loads. In reality, each functional failure mode
may have contributory components either in par-
allel to each other or in series. Also, the fault tree
is often expanded to show the resistances that
react against the loads. The analyst may construct
a tree for any point in the system, ranging from
the entire facility to any element within a sub-
system. Figure 6-2 is a fault tree for an entire
facility.
(1) When all of the elements that are to be
included in the fault tree have been identified and
diagrammed to show their relationship to each
other (this information is obtained from the func-
tional block diagram discussed in b above), then
the failure modes for each element should be iden-
tified if they bear some positive relationship to the
mechanical, radiative, thermal, and other thermo-
nuclear elements. The local environment, i.e., the
loads exciting each response leading to a failure
mode, should also be identified. The failure modes
and loads are then added to the fault tree as shown
in figure 6-2. More than one element, subsystem, or
system can be considered in the analysis. The lar-
ger the physical system involved, the more com-
plete will be the fault tree. However, the tree will
also become more complex. Initially, the fault trees
are constructed without regard to simplification
because their primary purpose is to provide a com-
plete (and perhaps redundant) description of the
system, its failure modes, the loads acting on it,
and the resistances.
(2) When constructing the fault trees, the over-
all complexity may be minimized by removing
superhard or supersoft systems, subsystems, or ele-
ments from consideration; and by beginning at the
lowest level of the tree that is practicable, i.e., at
the element level. Nevertheless, for a system, sub-
system, or element of any real complexity, it is
inevitable that the first construction will contain
redundancies and interdependencies that would not
be immediately obvious. A simplifying procedure is
required.
TM 5-858-6
Figure 6-1. Types of logic diagrams.
(a) Tree
U.S. Army Corps of Engineers
(b) Network
6-2
TM 5-858-6
Figure 6-2. Typical generalized fault tree.
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6-3
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e. Boolean equations. Fortunately, the fault tree
can be used to develop Boolean equations that will
reveal interdependencies and eliminate redundan-
cies. This is accomplished by writing the Boolean
equations for the original fault tree and then re-
ducing the equations to their simplest form. A new
fault tree can then be constructed from the new
Boolean equations, and this revision will be void of
redundant information.
(1) In order to implement Boolean algebra, the
fault trees are usually presented in the particular
form typified in figure 6-3. The symbols are called
"gates;" the Boolean logic depends on the type of
gate involved. Hammer (1972) describes the special-
ized fault tree and Boolean algebra. An application
to hardened systems is presented by Collins (1975).
(2) An extremely important feature of Boolean
algebra is that the equations can be used to des-
ignate the survival or failure probability of the
system under study. (See Collins, 1975.)
6-3. Elements of verification analysis.
a. Resistance. One of the principal purposes of
this volume has been to establish that resistance is
a random variable. The character of the load and
the resistance are expressed as uncertainty factors
that are defined as a measure of scatter (variance)
normalized to the mean-squared response. More-
over, uncertainty is generally composed of a ran-
dom component (a reflection of natural variation)
and a systematic component (an expression of ig-
norance). How these uncertainties can be deter-
mined and how survival probabilities can be com-
puted were discussed in paragraph 5-2.
b. Local load environment. The nuclear weapon
effects exciting a system usually can be considered
random variables, since free-field weapon effect
loads are transmitted through the parts of a fa-
cility whose transmission characteristics,
determined by its geometrical and material prop-
erties, are at best only statistically known. Hence,
the local environments are probabilistic, and are
modifications (amplification or attenuation) of one
or more of the free-field, nuclear weapon-effect
loads. If only the primary environment is known,
than either the local environment must be arbi-
trarily specified or it must be determined. If it is
to be determined, the values must be derived by
the use of transfer functions, which relate free-
field environments to local-load environments. Be-
cause of the nature of the real systems, the trans-
fer functions are also random variables. The rela-
tionship among these variables is shown in figure
6-4.
c. Transfer functions. Transfer functions link the
primary nuclear weapon-effect loads to the local
loads acting on the system, subsystem, or element
under study. When performing an actual verifica-
tion analysis of a system, the general procedure is
first to complete verification of critical elements,
then progress to subsystems, systems, and finally
the facility, in building-block fashion. In so doing,
however, defining the loads at the element level
becomes more difficult, since the analyst will not
yet have determined how the primary nuclear
weapon-effect loads have been modified by the ac-
tual intervening systems and subsystems. Thus, the
verification analyst either must utilize the existing
design loads or must develop transfer functions.
(1) Whichever method is used depends on the
particulars of the problem under investigation. For
example, if the design-load specification represents
the most advanced (best) estimate of the load, the
analyst may continue to use this as the load speci-
fication. However, if the outgoing verification anal-
yses indicate that the original estimate was in
error, a better estimate of the local loads would be
required. Later, as progress is made by solving the
fault tree equations, the transfer functions can be
corroborated by analyses; also new verification at
less comprehensive levels can be conducted when-
ever the ongoing analyses indicate that the trans-
fer functions were erroneously or incompletely
specified.
(2) It is again emphasized that transfer func-
tions have their own uncertainties, consisting of
random and systematic components. These uncer-
tainties add another variation to the local load
environment, beyond the variations (if any are as-
sumed) existing in the free-field nuclear-weapon
effect loads themselves.
6-4. Correlations.
a. An additional factor to be considered is that
local loads acting on a system, subsystem, or ele-
ment may be transmitted via one or more transfer
functions, in series or in parallel, that may be
correlated with each other. The simplest configura-
tion comes from Boolean equations derived from
the fault tree. Note that the Boolean algebra auto-
matically accounts for serial and parallel connec-
tions. However, it will not account for the degree
of correlation between transfer functions; these
must be calculated separately.
b. A given system may be suceptible to a number
of nuclear-weapon-effect loads. At the particular
point where verification is being performed, there
may be some degree of correlation between local
environments, transfer functions, or resistances.
6-4
TM 5-858-6
Figure 6-3. Typical Fault Tree with Network Logic Symbols
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The degree of correlation is specified by the cor-
relation coefficient p^. Correlation coefficients vary
in the range of l<p<l. If strong positive cor-
relation occurs, the system is more likely to survive
than if the variables were not correlated at all. On
the other hand, if strong negative correlation oc-
curs, the system is less likely to survive than if the
variables were not correlated at all. Therefore, in
evaluating equation 5-9 the correlation coefficients
between various elements of the local loads and the
resistance must be determined.
c. The covariance (which is a more general quan-
tity to be used in equation 5-4) is defined as
N
n O\T O"xr 1 s / A \/ A \
^nm Y n Y m = -/^ (y n -yn)(ym-ym)
JN l n=l
m=l
where Y n and Y m are any two of N variables cor-
responding to the resistance function or the load
function. The notation y indicates selected values of
the model representing the random variable Y, and
y is the mean of those selected values. The quan-
tity o y is the standard deviation of the variable Y.
Equation 5-7 is evaluated by randomly selecting
values for the variables y n and y m . For example, y n
may represent random values for the stiffness of
concrete, and y m may represen random values for
the damping properties of the same concrete. If the
stiffness and damping are totally uncorrelated (i.e.,
totally independent of each other), the quantity
within the summation of equation 5-7 will tend to
zero as N becomes large and Pnm0; on the other
hand, if the stiffness and damping are negatively
correlated (i.e., if selections of y n >7m are more
often than not produce the condition that y m <y m ,
then the quantity within the summation will tend
toward a negative number and Py will be a nega-
tive number for large values of N. Coversely, posi-
tive correlation (p nm >0) would indicate that as the
concrete stiffness increases, the damping also in-
creases. The limiting conditions for the correlation
coefficient are -1 <p nm <1.
6-7
APPENDIX A
BINOMIAL DISTRIBUTION
This appendix contains two tables in support of
statistical analysis, Chapter 3. Use Table A-l in
determining the probability of s=r successes in n
trials, table A-2 for s>:r successes in n trials.
A-l
TM 5-858-6
TABLE A-l. INDIVIDUAL TERMS
PROBABILITY OF REALIZING s = r SUCCESSES IN n TRIALS
j^ t T n ~" v *
> PJ r I (n - r) ! ^
p
n = 2
r = 1
n s 2
r =
n = 3
r = 2
n = 3
r = 1
n * 3
r =
n = 4
r = 3
P
.01
.0196
.9801
.0003
.0294
.9703
.0000
.01
.02
.0392
.9604
.0012
.0576
.9412
.0000
.02
.03
.0562
.9409
.0026
,0847
.9127
.0001
.03
.04
.0768
.9216
.0046
.1106
.6847
.0002
.04
.05
.0950
.9025
.0071
.1354
.8574
.0005
.05
.06
.1126
.8636
.0102
.1590
.8306
.0008
.06
.07
.1302
.8649
.0137
.1816
.8044
.0013
.07
.06
.1472
.6464
.0177
.2031
.7787
,0019
.08
.09
.1636
.8261
.0221
.2236
.7536
.0027
.09
.10
.1600
.6100
.0270
.2430
.7290
.0036
.10
.11
.1958
.7921
.0323
.2614
.7050
.0047
.11
.12
.2112
.7744
.0380
.2788
.6815
.0061
.12
.13
.2262
.7569
.0441
.2952
.6585
.0076
.13
.14
.2408
.7396
.0506
.3106
.6361
.0094
.14
.15
.2550
.7225
.0574
.3251
.6141
,0115
.15
.16
.2686
.7056
.0645
.3387
.5927
.0138
.16
.17
.2622
.6669
.0720
.3513
.5718
.0163
.17
.18
.2952
.6724
.0797
.3631
.5514
.0191
.Id
.19
.3078
.6561
.0877
.3740
.5314
.0222
.19
.20
.3200
.6400
.0960
.3840
.5120
.0256
.20
.21
.3318
.6241
.1045
.3932
.4930
,0293
,21
.22
.3432
.6064
.1133
.4015
.4746
.0332
.22
.23
.3542
.5929
.1222
.4091
.4565
,0375
.23
.24
.3646
.5776
.1313
.4159
.4390
,0420
.24
.25
.3750
.5625
.1406
.4219
.4219
.0469
.25
.26
.3846
.5476
.1501
.4271
.4052
.0520
.26
.27
.3942
.5329
.1597
.4316
.3890
.0575
.27
.26
.4032
.5184
.1693
.4355
.3732
.0632
.26
.29
.4116
.5041
.1791
.4386
.3579
.0693
.29
.30
.4200
.4900
.1890
.4410
.3430
.0756
.30
.31
.4278
.4761
.1989
.4428
.3285
.0622
.31
.32
.4352
.4624
.2089
.4439
.3144
.0891
.32
.33
.4422
.4469
.2189
.4444
.3006
.0963
.33
.34
.4468
.4356
.2269
.4443
.2875
.1038
.34
.35
.4550
.4225
.2389
.4436
.2746
.1115
.35
.36
.4608
.4096
.2468
.4424
.2621
.1194
.36
.37
.4662
.3969
.2567
.4406
.2500
.1276
.37
.36
.4712
.3844
.2666
.4382
.2363
.1361
.38
.39
.4756
.3721
.2783
.4354
.2270
.1447
.39
.40
.4600
.3600
.2680
.4320
.2160
.1536
.40
.41
.4638
.3461
.2975
.4262
.2054
.1627
.41
.42
.4872
.1364
.3069
.4239
.1951
.1719
.42
.43
.4902
.3249
.3162
.4191
.1852
.1813
.43
.44
.4928
.3136
.3252
.4140
.1756
.1908
.44
.45
.4950
.3025
.3341
.4064
.1664
.2005
.45
.46
.4966
.2916
.3426
.4024
.1575
.2102
.46
.47
.4982
.2609
.3512
.3961
.1489
.2201
.47
.46
.4992
.2704
.3594
.3894
.1406
.2300
.48
.49
.4998
.2601
.3674
.3623
.1327
.2400
.49
.50
.5000
.2500
.3750
.3750
.1250
.2500
.50
U.S. Army Corps of Engineers
A-2
TABLE A-l. (CONTINUED)
TM 5-858-6
p
n = 4
r = 2
n = 4
r = 1
n = 4
r =
n s= 5
r = 4
n = 5
r = 3
n = 5
r = 2
P
.01
.0006
.0388
.9606
.0000
.0000
.0010
.01
02
.0023
.0753
.9224
.0000
.0001
.0038
.02
.03
.0051
.1095
.8853
.0000
.0003
.0062
.03
.04
.0088
.1416
.8493
.0000
.0006
.0142
.04
.05
.0135
.1715
.8145
.0000
.0011
.0214
.05
.06
.0191
.1993
.7807
.0001
.0019
.0299
.06
.07
.0254
.2252
.7481
.0001
.0030
.0394
.07
.08
.0325
.2492
.7164
.0002
.0043
.0498
.06
.09
.0402
.2713
.6857
.0003
.0060
.0610
.09
.10
.0466
.2916
.6561
.0004
.0061
.0729
.10
.11
.0575
.3102
.6274
.0007
.0105
.0853
.11
.12
.0669
.3271
.5997
.0009
.0134
.0981
.12
.13
.0767
.3424
.5729
.0012
.0166
.1113
.13
.14
.0870
.3562
.5470
.0017
.0203
.1247
.14
.15
.0975
.3685
.5220
.0022
.0244
.1362
.15
.16
.1084
.3793
.4979
.0028
.0289
.1517
.16
.17
.1195
.3888
.4746
.0035
.0336
.1652
.17
.18
.1307
.3970
.4521
.0043
.0392
.1786
.18
.19
.1421
.4039
.4305
.0053
.0450
.1919
.19
.20
.1536
.4096
.4096
.0064
.0512
.2048
.20
.21
.1651
.4142
.3895
.0077
.0578
.2174
.21
.22
.1767
.4176
.3702
.0091
.0646
.2297
.22
.23
.1882
.4200
.3515
.0108
.0721
.2415
.23
.24
.1996
.4214
.3336
.0126
.0798
.2529
.24
.25
.2109
.4219
.3164
.0146
.0879
.2637
.25
.26
.2221
.4214
.2999
.0169
.0962
.2739
.26
.27
.2331
.4201
.2840
.0194
.1049
.2836
.27
.28
.2439
.4180
.2687
.0221
.1138
.2926
.28
.29
.2544
.4152
.2541
.0251
.1229
.3010
.29
.30
.2646
.4116
.2401
.0283
.1323
.3067
.30
.31
.2745
.4074
.2267
.0319
.1416
.3157
.31
.32
.2841
.4025
,2138
.0357
.1515
.3220
.32
.33
.2933
.3970
.2015
.0397
.1613
.3275
.33
.34
.3021
.3910
.1897
.0441
.1712
.3323
.34
.35
.3105
.3845
.1785
.0488
.1611
.3364
.35
.36
.3185
.3775
.1678
.0537
.1911
.3397
.36
.37
.3260
.3701
.1575
.0590
.2010
.3423
.37
.38
.3330
.3623
.1478
.0646
.2109
.3441
.38
.39
.3396
.3541
.1385
.0706
.2207
.3452
.39
.40
.3456
.3456
.1296
.0768
.2304
.3456
.40
.41
.3511
.3368
.1212
.0834
.2399
.3452
.41
.42
.3560
.3278
.1132
.0902
.2492
.3442
.42
.43
.3604
.3185
.1056
.0974
.2563
.3424
.43
.44
.3643
.3091
.0983
.1049
.2671
.3400
.44
.45
.3675
.2995
.0915
.1128
.2757
.3369
.45
.46
.3702
.2897
.0850
.1209
.2838
.3332
.46
.47
.3723
.2799
.0789
.1293
.2916
.3289
.47
.48
.3738
.2700
.0731
.1380
.2990
.3240
.46
.49
.3747
.2600
.0677
.1470
.3060
.3185
.49
.50
.3750
.2500
.0625
.1562
.3125
.3125
.50
A-3
TM 5-858-6
TABLE A-l. (CONTINUED)
p
n = 5
r = 1
n = 5
r =
n = 6
r = 5
n = 6
r = 4
n = 6
r = 3
n = 6
r = 2
P
.01
.0480
.9510
.0000
0000
.0000
.0014
.01
.02
.0922
.9039
.0000
.0000
.0002
.0055
02
.03
.1328
.8587
.0000
0000
.0005
.0120
03
.04
.1699
.8154
0000
.0000
.0011
.0204
.04
.05
.2036
.7738
.0000
0001
0021
.0305
05
.06
.2342
.7339
.0000
.0002
0036
.0422
06
.07
.2618
.6957
.0000
0003
0055
.0550
07
.08
.2866
-6591
0000
.0005
.0080
.0668
.08
.09
.3086
.6240
.0000
.0008
.0110
.0833
09
.10
.3281
.5905
.0001
0012
.0146
.0984
10
.11
.3451
.5584
.0001
.0017
.0186
.1139
11
.12
.3598
.5277
.0001
0024
.0236
.1295
.12
.13
.3724
4984
.0002
0032
.0289
.1452
.13
.14
.3829
.4704
.0003
0043
.0349
.1608
14
.15
.3915
.4437
.0004
.0055
.0415
.1762
15
.16
.3983
.4182
.0005
.0069
.0486
1912
.16
.17
.4034
.3939
.0007
0086
.0562
.2057
.17
.18
.4069
.3707
.0009
0106
.0643
.2197
.18
.19
.4089
.3487
.0012
0128
0729
.2331
19
.20
.4096
.3277
.0015
.0154
.0819
.2458
20
.21
.4090
.3077
.0019
.0182
.0913
.2577
.21
.22
.4072
.2887
.0024
0214
.1011
.2687
22
.23
.4043
.2707
.0030
0249
.1111
.2789
.23
.24
.4003
.2536
.0036
0287
.1214
.2882
.24
.25
.3955
.2373
.0044
0330
.1318
.2966
.25
.26
.3898
.2219
.0053
0375
1424
.3041
.26
.27
.3834
.2073
.0063
.0425
.1531
.3105
.27
.28
.3762
.1935
.0074
.0478
.1639
.3160
28
.29
.3685
.1804
.0087
.0535
.1746
.3206
29
.30
.3602
.1681
.0102
.0595
.1852
.3241
.30
.31
.3513
.1564
.0119
.0660
.1957
.3267
.31
.32
.3421
.1454
.0137
.0727
.2061
.3284
.32
.33
.3325
.1350
.0157
.0799
.2162
.3292
.33
.34
.3226
.1252
.0180
.0873
.2260
.3290
.34
.35
.3124
.1160
.0205
0951
.2355
.3280
.35
.36
.3020
.1074
.0232
.1032
.2446
.3261
.36
.37
.2914
.0992
.0262
1116
.2533
.3235
.37
.38
.2808
.0916
.0295
.1202
.2616
.3201
.38
.39
.2700
.0845
0330
.1291
,2693
3159
.39
.40
.2592
.0778
,0369
.1382
.2765
3110
.40
.41
.2484
.0715
.0410
.1475
.2831
.3055
.41
.42
.2376
.0656
.0455
.1570
.2891
.2994
42
.43
.2270
.0602
,0503
.1666
.2945
.2928
43
.44
.2164
.0551
,0554
.1763
.2992
.2856
.44
.45
.2059
.0503
.0609
.1861
.3032
.2780
.45
.46
.1956
.0459
.0667
.1958
.3065
.2699
.46
.47
.1854
.0418
.0729
.2056
.3091
.2615
.47
.48
.1755
.0380
.0795
.2153
.3110
.2527
.48
.49
.1657
.0345
.0864
.2249
.3121
.2436
.49
.50
.1563
.0313
.0937
.2344
.3125
.2344
.50
A-4
TABLE A-l. (CONTINUED)
TM 5-858-6
p
n = 6
r = 1
n = 6
r =
n = 7
r = 6
n = 7
r = 5
n = 7
r = 4
n = 7
r = 3
P
01
.0571
.9415
.0000
.0000
.0000
.0000
.01
.02
.1085
.8858
.0000
.0000
.0000
.0003
.02
.03
.1546
.8330
.0000
.0000
.0000
.0003
.03
.04
.1957
.7828
.0000
.0000
.0001
.0019
.04
.05
.2321
.7351
.0000
.0000
.0002
.0036
.05
.06
.2642
.6899
.0000
.0000
.0004
.0059
.06
.07
.2922
'.6470
.0000
.0000
.0007
.0090
.07
.08
.3164
.6064
.0000
.0001
.0011
.0128
.03
.09
.3370
.5679
.0000
.0001
.0017
.0175
.09
.10
.3543
.5314
.0000
.0002
.0026
.0230
.10
.11
.3685
.4970
.0000
.0003
.0036
.0292
.11
.12
.3800
.4644
.0000
.0004
.0049
.0363
.12
.13
.3888
.4336
.0000
.0006
.0066
.0441
.13
.14
.3952
.4046
.0000
.0008
.0036
.0525
.14
.15
.3993
.3771
.0001
.0012
.0109
.0617
.15
.16
.4015
.3513
.0001
.0016
.0136
.0714
.16
.17
4018
.3269
.0001
.0021
.0167
.0816
.17
.16
.4004
.3040
.0002
.0027
.0203
.0923
.13
.19
.3975
.2824
.0003
.0034
.0242
.1033
.19
.20
.3932
.2621
.0004
.0043
.0287
.1147
.20
.21
.3877
.2431
.0005
.0054
.0336
.1263
.21
.22
.3811
.2252
.0006
.0066
.0389
.1379
.22
.23
.3735
.2084
.0008
.0080
.0447
.1497
.23
.24
.3651
.1927
.0010
.0097
.0510
.1614
.24
.25
.3560
.1780
.0013
.0115
.0577
.1730
.25
.26
.3462
.1642
.0016
.0137
.0648
.1845
.26
.27
.3358
.1513
.0020
.0161
.0724
.1956
.27
.28
.3251
.1393
.0024
.0187
.0803
.2065
.28
.29
.3139
.1261
.0030
.0217
.0886
.2169
.29
.30
.3025
.1176
.0036
.0250
,0972
.2269
.30
.31
.2909
.1079
.0043
.0286
.1062
.2363
.31
.32
.2798
.0989
.0051
.0326
.1154
.2452
.32
.33
.2673
.0905
.0061
.0369
.1243
.2535
.33
.34
.2555
.0827
.0071
.0416
.1345
.2610
.34
.35
.2437
.0754
.0084
.0466
.1442
.2679
.35
.36
.2319
.0687
,0098
.0520
.1541
.2740
.36
.37
.2203
.0685
.0113
.0578
.1640
.2793
.37
.38
.2089
.0568
.0131
.0640
.1739
.2838
.38
.39
.1976
.0515
.0150
.0705
.1838
.2875
.39
.40
.1866
.0467
.0172
.0774
.1935
.2903
.40
.41
.1759
.0422
.0196
.0847
.2031
.2923
1
.42
.1654
.0381
.0223
.0923
.2125
.2934
.42
.43
.1552
.0343
.0252
.1003
.2216
.2937
.43
.44
.1454
.0308
.0284
.1036
.2304
.2932
.44
.45
.1359
.0277
.0320
.1172
.2388
.2918
.45
.46
.1267
.0248
.0358
.1261
.2468
.2897
.46
.47
.1179
.0222
.0400
.1353
.2543
.2867
.47
.48
.1095
.0198
.0445
.1447
.2612
830
.48
.49
.1014
.0176
.0494
.1543
.2676
.2736
.49
.50
.0938
.0156
.0547
.1641
.2734
.2734
.50
TM 5-858-6
TABLE A-l. (CONTINUED)
p
n = 7
r = 2
n = 7
r = 1
n = 7
r =
n = 8
r = 7
n = 8
r = 6
n = 8
r = 5
P
.01
.0020
.0659
.9321
.0000
.0000
.0000
01
.02
.0076
.1240
.8681
.0000
.0000
.0000
.02
.03
.0162
.1749
,8080
.0000
.0000
.0000
.03
.04
.0274
.2192
,7514
.0000
.0000
.0000
.04
.05
.0406
.2573
.6983
.0000
.0000
.0000
.05
.06
.0555
.2897
.6485
.0000
.0000
.0000
.06
.07
.0716
.3170
,6017
.0000
.0000
.0001
.07
.08
0886
.3396
.5578
.0000
.0000
.0001
.08
.09
.1061
.3578
.5168
.0000
.0000
.0002
.09
.10
.1240
.3720
,4783
.0000
.0000
.0004
10
.11
.1419
.3827
.4433
.0000
.0000
.0006
11
.12
.1596
.3901
.4087
.0000
.0001
.0009
.12
.13
.1769
.3946
.3773
.0000
.0001
.0014
.13
.14
.1936
.3965
,3479
.0000
.0002
.0019
14
.15
.2097
.3960
.3206
.0000
.0002
.0026
15
.16
.2248
.3935
.2951
.0000
.0003
.0035
.16
.17
.2391
.3891
,2714
.0000
.0005
.0045
17
.16
.2523
.3830
.2493
.0000
.0006
.0058
18
.19
.2643
.3756
.2288
.0001
.0009
.0074
.19
.20
.2753
.3670
.2097
.0001
.0011
.0092
20
.21
.2850
.3573
.1920
.0001
.0015
.0113
.21
.22
.2935
.3468
.1757
.0002
.0019
.0137
22
.23
.3007
.3356
.1605
.0002
.0025
.0165
.23
.24
.3067
.3237
.1465
.0003
.0031
.0196
.24
.25
.3115
.3115
,1335
.0004
.0038
.0231
25
.26
.3150
.2969
.1215
.0005
.0047
.0270
26
.27
.3174
.2860
.1105
.0006
.0058
.0313
.27
.28
.3186
.2731
.1003
.0008
.0070
.0360
.28
.29
.3186
.2600
.0910
.0010
.0084
.0411
.29
.30
.3177
.2471
.0824
.0012
.0100
.0467
30
.31
.3156
.2342
,0745
.0015
.0118
.0527
.31
.32
.3127
.2215
,0672
.0019
.0139
.0591
.32
.33
.3088
.2090
.0606
.0023
.0162
.0659
33
.34
.3040
.1967
.0546
.0028
.0188
.0732
34
.35
.2985
.1848
.0490
.0033
.0217
.0808
.35
.36
.2922
.1732
.0440
.0040
.0250
.0888
36
.37
.2853
.1619
.0394
.0048
.0285
.0971
37
.36
.2778
.1511
.0352
.0057
.0324
.1058
38
.39
.2698
.1407
.0314
.0067
.0367
.1147
.39
.40
.2613
.1306
.0280
.0079
.0413
.1239
40
.41
.2524
.1211
.0249
.0092
.0463
.1332
.41
.42
.2431
.1119
.0221
.0107
.0517
.1428
.42
.43
.2336
.1032
.0195
.0124
.0575
.1525
.43
.44
.2239
.0950
,0173
.0143
.0637
.1622
.44
.45
.2140
.0872
.0152
.0164
.0703
.1719
.45
.46
.2040
.0798
.0134
.0168
.0774
.1816
.46
.47
.1940
.0729
.0117
.0215
.0848
.1912
.47
.48
.1840
.0664
.0103
.0244
.0926
.2006
.48
.49
.1740
.0604
.0090
.0277
.1008
.2098
.49
.50
.1641
.0547
.0078
.0312
.1094
.2187
.50
A-6
TABLE A-l. (CONTINUED)
TM 5-858-6
p
n = 8
r = 4
n = 8
r = 3
n = 8
r = 2
n = 8
r = 1
n = 8
r =
n = 9
r = 8
P
.01
.0000
.0001
.0026
.0746
.9227
.0000
.01
.02
.0000
.0004
.0099
.1389
.6506
, 0000
.02
.03
.0001
.0013
.0210
.1939
.7837
.0000
.03
.04
.0002
.0029
.0351
.2405
.7214
.0000
.04
.05
.0004
.0054
.0515
.2793
.6634
.0000
.05
.06
.0007
.0089
.0695
.3113
.6096
.0000
.06
.07
.0013
.0134
.0686
.3370
.5596
.0000
.07
.06
.0021
.0169
.1087
.3570
.5132
.0000
.08
.09
.0031
.0255
.1266
.3721
.4703
.0000
.09
.10
.0046
.0331
.1466
.3626
.4305
.0000
.10
.11
.0064
.0416
.1664
.3893
.3937
.0000
.11
.12
0087
.0511
.1872
.3923
.3596
.0000
.12
.13
.0115
.0613
,2052
.3923
.3282
.0000
.13
.14
.0147
.0723
.2220
.3897
.2992
.0000
.14
.IS
.0185
.0839
.2376
.3847
.2725
.0000
.15
.16
.0226
.0959
.2518
.3777
.2479
.0000
.16
.IT
.0277
.1084
.2646
.3691
.2252
.0000
.17
.18
.0332
.1211
.2758
.3590
.2044
.0000
.18
.19
.0393
.1339
.2855
.3477
.1653
.0000
.19
.20
.0459
.1466
.2936
.3355
.1676
.0000
.20
.21
.0530
.1596
.3002
.3226
.1517
.0000
.21
.22
.0607
.1722
.3052
.3092
.1370
.0000
.22
.23
.0689
.1844
.3067
.2953
.1236
.0001
.23
.24
.0775
.1963
.3108
.2812
.1113
.0001
.24
.25
.0665
.2076
.3115
.2670
.1001
.0001
.25
.26
.0959
.2184
.3108
.2527
.0899
0001
.26
.27
.1056
.2285
.3089
.2366
.0806
.0002
.27
.28
.1156
.2379
.3058
.2247
.0722
.0002
.28
.29
.1256
.2464
.3017
.2110
.0646
.0003
.29
.30
.1361
.2541
.2965
.1977
.0576
.0004
.30
.31
.1465
.2609
.2904
.1847
.0514
.0005
.31
.32
.1569
.2666
.2635
.1721
.0457
.0007
.32
.33
.1673
.2717
.2758
.1600
.0406
.0006
.33
.34
.1775
.2756
.2675
.1464
.0360
.0011
.34
.35
.1675
.2786
.2587
.1373
.0319
.0013
.35
.36
.1973
.2605
.2494
.1267
.0261
.0016
.36
.37
.2067
.2615
.2397
.1166
.0246
.0020
.37
.36
.2157
.2815
.2297
.1071
0218
.0024
.38
.39
.2242
.2606
.2194
.0981
.0192
.0029
.39
.40
2322
.2757
.2090
.0896
.0166
.0035
.40
.41
.2397
.2759
.1985
.0616
.0147
.0042
.41
.42
.2465
.2723
.1680
.0742
.0128
.0051
.42
.43
.2526
.2679
.1776
.0672
.0111
.0060
.43
.44
.2580
.2627
.1672
.0606
.0097
.0071
.44
.45
.2627
.2566
.1569
.0548
.0084
.0063
.45
.46
.2665
.2503
.1469
.0493
.0072
.0097
.46
.47
.2695
.2431
.1371
.0442
.0062
.0114
.47
.46
.2717
.2355
.1275
.0395
.0053
.0132
.48
.49
.2730
.2273
.1183
.0352
.0046
.0153
.49
.50
.2734
.2186
.1094
.0313
.0039
.0176
.50
A-7
TM 5-858-6
TABLE A-l. (CONTINUED)
p
n = 9
r = 7
n = 9
r = 6
n = 9
r = 5
n = 9
r = 4
n = 9
r = 3
n = 9
r = 2
P
.01
.0000
.0000
.0000
.0000
.0001
.0034
.01
.02
.0000
.0000
.0000
.0000
.0006
.0125
.02
.03
.0000
.0000
.0000
.0001
.0019
.0262
.03
.04
.0000
.0000
.0000
.0003
.0042
.0433
.04
.05
.0000
.0000
.0000
.0006
.0077
.0629
.05
.06
.0000
.0000
.0001
.0012
.0125
.0840
.06
.07
.0000
.0000
.0002
.0021
.0186
.1061
.07
.08
.0000
.0000
.0003
.0034
.0261
.1285
.08
.09
.0000
.0000
.0005
.0052
.0348
.1507
.09
.10
.0000
.0001
.0008
.0074
.0446
.1722
.10
.11
.0000
.0001
.0013
.0103
.0556
.1927
.11
.12
.0000
.0002
.0019
.0138
.0674
.2119
.12
.13
.0000
.0003
.0027
.0179
.0800
.2295
.13
.14
.0000
.0004
.0037
.0228
.0933
.2455
.14
.15
.0000
.0006
.0050
.0283
.1069
.2597
.15
.16
.0001
.0008
.0066
.0345
.1209
.2720
.16
.17
.0001
.0012
.0085
.0415
.1349
.2823
.17
.16
.0001
.0016
.0108
.0490
.1489
.2908
.18
.19
.0002
.0021
.0134
.0573
.1627
.2973
.19
.20
.0003
.0028
.0165
.0661
.1762
.3020
.20
.21
.0004
.0036
.0200
.0754
.1891
.3049
.21
.22
.0005
.0045
.0240
.0852
.2014
.3061
.22
.23
.0007
.0057
.0285
.0954
.2130
.3056
.23
.24
.0010
.0070
.0335
.1060
.2238
.3037
.24
.25
.0012
.0087
.0389
.1168
.2336
.3003
.25
.26
.0016
.0105
.0449
.1278
.2424
.2957
.26
.27
.0020
.0127
.0513
.1388
.2502
.2899
.27
.28
.0025
.0151
.0583
.1499
.2569
.2831
.28
.29
.0031
.0179
.0657
.1608
.2624
.2754
.29
.30
.0039
.0210
.0735
.1715
.2668
.2668
.30
.31
.0047
.0245
.0818
.1820
.2701
.2576
.31
.32
.0057
.0284
.0904
.1921
.2721
.2478
.32
.33
.0069
.0326
.0994
.2017
.2731
.2376
.33
.34
.0082
.0373
.1086
.2109
.2729
.2270
.34
.35
.0098
.0424
.1181
.2194
.2716
.2162
.35
.36
.0116
.0479
.1278
.2272
.2693
.2052
.36
.37
.0136
.0539
.1376
.2344
.2660
.1941
.37
.38
.0158
.0603
.1475
.2407
.2618
.1831
.38
.39
.0184
.0671
.1574
.2462
.2567
.1721
.39
.40
.0212
.0743
.1672
.2508
.2508
.1612
.40
*41
.0244
.0819
.1769
.2545
.2442
.1506
.41
.42
.0279
.0900
.1863
.2573
.2369
.1402
.42
.43
.0318
.0983
.1955
.2592
.2291
.1301
.43
.44
.0360
.1070
.2044
.2601
.2207
.1204
.44
.45
.0407
.1160
.2128
.2600
.2119
.1110
.45
.46
.0458
.1253
.2207
.2590
.2027
.1020
.46
.47
.0512
.1348
.2280
.2571
.1933
.0934
.47
.48
.0571
.1445
.2347
.2543
.1837
.0853
.48
.49
.0635
.1542
.2408
.2506
.1739
.0776
.49
.50
.0703
.1641
.2461
.2461
.1641
.0703
.50
A-8
TABLE A-l. (CONTINUED)
TM 5-858-6
p
n = 9
r = 1
n = 9
r =
n = 10
r = 9
n = 10
r = 8
n = 10
r = 7
n = 10
r = 6
P
.01
.0830
.9135
.0000
.0000
.0000
.0000
.01
02
.1531
.8337
.0000
.0000
.0000
. 0000
.02
.03
.2116
.7602
.0000
.0000
.0000
.0000
.03
.04
.2597
.6925
.0000
.0000
.0000
.0000
.04
.05
.2985
.6302
.0000
.0000
.0000
.0000
.05
.06
.3292
.5730
.0000
.0000
.0000
.0000
.06
.07
.3525
.5204
.0000
.0000
.0000
.0000
.07
.08
.3695
.4722
.0000
.0000
.0000
.0000
.08
.09
.3809
.4279
.0000
.0000
.0000
.0001
.09
.10
.3874
.3874
.0000
.0000
.0000
.0001
.10
.11
.3897
.3504
.0000
.0000
.0000
.0002
.11
.12
.3884
.3165
.0000
.0000
.0000
.000^
.12
.13
.3840
.2855
.0000
.0000
.0000
.0006
.13
.14
.3770
.2573
.0000
.0000
.0001
.0009
.14
IS
.3679
.2316
.0000
.0000
.0001
.0012
.15
.16
.3569
.2082
.0000
.0000
.0002
.0018
.16
.17
.3446
.1869
.0000
.0000
.0003
.0024
.17
.18
.3312
.1676
.0000
.0000
.0004
.0032
.ia
.19
.3169
.1501
.0000
.0001
.0006
.0043
.19
.20
3020
.1342
.0000
.0001
.0008
.0055
.20
.21
.2867
.1199
.0000
.0001
.0011
.0070
.21
.22
.2713
.1069
.0000
.0002
.0014
.0088
.22
.23
.2556
.0952
.0000
.0002
.0019
.0109
.23
.24
.2404
.0846
.0000
.0003
.0024
.0134
.24
.25
.2253
.0751
.0000
.0004
.0031
.0162
.25
.26
.2104
.0665
.0000
.0005
.0039
.0195
.26
.27
.1960
.0589
.0001
.0007
.0049
.0231
.27
.28
.1820
.0520
.0001
.0009
.0060
.0272
.28
.29
.1685
.0458
.0001
.0011
.0074
.0317
.29
.30
.1556
.0404
.0001
.0014
.0090
.0368
.30
.31
,1433
.0355
.0002
.0018
.0108
.0422
.31
.32
.1317
.0311
.0002
.0023
.0130
.0482
.32
.33
.1206
.0272
.0003
.0028
.0154
.0547
.33
.34
.1102
.0238
.0004
.0035
.Oldl
.0616
.34
.35
.1004
.0207
.0005
.0043
.0212
.0689
.35
.36
.0912
.0130
.0006
.0052
.0347
.0767
.36
.37
.0826
.0156
.0008
.0063
.0285
.0849
.37
.38
.0747
.0135
.0010
.0075
.0327
.0934
.38
.39
.0673
.0117
.0013
.0090
.0374
1Q23
.39
.40
.0605
.0101
.0016
.0106
.0425
.1115
.40
.41
.0542
.0087
.0019
.0125
.0430
.1209
.41
.42
.0484
.0074
.0024
.0147
.0540
.1304
.43
.43
.0431
.0064
.0029
.0171
.0604
.1401
.43
.44
.0383
.0054
.0035
.0198
.0673
.1499
.44
.45
.0339
.0046
.0042
.0229
.0746
.1596
.45
.46
.0299
.0039
.0050
.0263
.0824
.1692
.46
.47
.0263
.0033
.0059
.0301
.0905
.1786
.47
.48
.0231
.0028
.0070
.0343
..0991
.1878
.48
.49
.0202
.0023
.0063
.0389
.1080
.1966
.49
.50
.0176
.0020
.0098
.0439
.1172
.051
.50
A-9
TM 5-858-6
TABLE A-l. CONCLUDED)
p
n = 10
r ~ 5
n 10
r 4
n * 10
r = 3
n ~ 10'
r = 2
n = 10
r = 1
n B 10
r =
P
01
.0000
.0000
.0001
.0042
.0914
.9044
.01
.03
.0000
.0000
.0006
.0153
.1667
.8171
.02
.03
.0000
.0001
.0026
.0317
.2281
.7374
.03
.04
.0000
.0004
.0056
.0519
.2770
.6648
.04
.05
.0001
.0010
.0105
.0746
.3151
.5967
.05
.06
.0001
.0019
.0166
.0968
.3438
.5386
.06
.07
.0003
.0033
.0246
.1234
.3643
.4640
.07
.06
.0005
.0052
.0343
.1478
.3777
.4344
.06
.09
.0009
.0076
.0452
.1714
.3851
.3894
.09
.10
.0015
.0112
.0574
.1937
.3874
.3487
.10
.11
.0023
.0153
.0706
.2143
.3654
.3118
.11
.12
.0033
.0202
.0847
.2330
.3798
.2785
.12
.13
.0047
.0260
.0995
.2496
.3712
.2464
.13
.14
.0064
.0326
.1146
.2639
.3603
.2213
.14
.15
0065
.0401
.1296
.2759
.3474
.1969
.15
.16
.0111
.0463
.1450
.2656
.3331
.1749
.16
.17
.0141
.0573
.1600
.2929
.3176
.1552
.17
.16
.0177
.0670
.1745
.2960
.3017
.1374
.18
.19
.0216
.0773
.1683
.3010
.2852
.1216
.19
.20
.0264
.0661
.2013
.3020
.2684
.1074
.20
.21
.0317
.0993
.2134
.3011
.2517
.0947
.21
.22
.0375
.1106
.2244
.2964
.2351
.0634
.22
.23
.0439
.1225
.2343
.2942
.2188
.0733
.23
.24
.0509
.1343
.2429
.2885
.2030
.0643
.24
.25
.0564
.1460
.2503
.2816
.1877
.0563
.25
.26
.0664
.1576
.2563
.2735
.1730
.0492
.26
.27
.0750
.1669
.2609
.2646
.1590
.0430
.27
.26
.0639
.1798
.2642
.2546
.1456
.0374
.28
.29
.0933
.1903
.2662
.2444
.1330
.0326
.29
.30
.1029
.2001
.2666
.2335
.1211
.0262
.30
.31
.1128
.2093
.2662
.2222
.1099
.0245
.31
.32
.1229
.2177
.2644
.2107
.0995
.0211
.32
.33
.1332
.2253
.2614
.1990
.0698
.0182
.33
.34
.1434
.2320
.2573
.1873
.0808
.0157
.34
.35
.1536
.2377
.2522
.1757
,0725
.0135
.35
.36
.1636
.2424
.2462
.1642
.0649
.0115
.36
.37
.1734
.2461
.2394
.1529
.0576
.0098
.37
.38
.1629
.2487
.2319
.1419
.0514
.0064
.38
.39
.1920
.2503
.2237
.1312
.0456
.0071
.39
.40
.2007
.2506
.2150
.1209
.0403
.0060
.40
.41
.2067
.2503
.2056
.1111
.0355
.0051
.41
.42
.2162
.2466
.1963
.1017
.0312
.0043
.42
.43
.2229
.2462
.1665
.0927
.0273
.0036
.43
.44
.2269
.2427
,1765
.0643
.0238
.0030
.44
.45
.2340
.2364
.1665
.0763
.0207
.0025
.45
.46
.2363
.2331
.1564
.0666
.0180
.0021
.46
.47
.2417
.2271
.1464
.0619
.0155
.0017
.47
.46
.2441
.2204
.1364
.0554
.0133
.0014
.48
.49
.2456
.2130
.1267
.0494
.0114
.0012
.49
.50
.2461
.2051
.1172
.0439
.0096
.0010
.50
A-10
TM 5-858-6
TABLE A- 2. PARTIAL SUMS
PROBABILITY OF REALIZING s > r SUCCESSES IN n TRIALS
n
E,/.. p]
s n-s
S
P
n = 2
r = 2
n = 2
r = 1
n = 3
r = 3
n = 3
r = 2
n = 3
r = 1
n = 4
r * 4
P
01
.0001
.0199
.0000
.0003
.0297
.0000
.01
02
.0004
.0396
.0000
.0012
,0586
.0000
.02
.03
.0009
.0591
.0000
.0026
.0873
.0000
.03
.04
.0016
.0764
.0001
.0047
,1153
.0000
.04
.05
,0025
.0975
.0001
,0073
,1426
.0000
.05
.06
.0036
.1164
.0002
.0104
1694
.0000
.06
.07
.0049
.1351
.0003
.0140
.1956
0000
.07
.06
.0064
.1536
.0005
.0162
.2213
,0000
.08
.09
.0061
.1719
.0007
.0226
.2464
.0001
09
.10
.0100
.1900
.0010
.0260
.2710
0001
10
.11
.0121
.2079
.0013
.0336
.2950
.0001
.11
.13
.0144
.2256
,0017
.0397
.3185
0002
12
.13
.0169
.2431
.0022
,0463
.3415
.0003
.13
.14
.0196
.2604
.0027
.0533
.3639
.0004
14
.15
.0225
.2775
.0034
.0607
.3859
.4)005
.15
.16
.0256
.2944
.0041
.0666
.4073
.0007
16
.17
.0289
.3111
,0049
.0769
.4282
,0003
.17
.ia
.0324
.3276
.0056
,0655
.4466
.0010
.18
.19
.0361
.3439
.0069
,0946
.4666
.0013
.19
.20
.0400
.3600
.0060
.1040
.4680
.0016
.20
.21
.0441
.3759
.0093
,1136
.5070
.0019
.21
.22
.0464
.3916
.0106
,1239
.5254
,0023
.22
.23
.0529
.4071
.0122
.1344
.5435
.0026
.23
24
.0576
.4224
.0138
.1452
5610
.0033
24
.25
.0625
.4375
.0156
.1562
,5781
.0039
25
.26
0676
.4524
.0176
.1676
.5946
.0046
.26
.27
.0729
.4671
.0197
.1793
.6110
,0053
27
.26
.0764
.4616
.0220
.1913
.6266
.0061
28
.29
.0841
.4959
.0244
.2035
.6421
.0071
29
.30
.0900
.5100
.0270
.2160
.6570
.0081
.30
.31
.0961
.5239
.0296
.2287
.6715
,0092
31
32
.1024
.5376
.0326
.2417
,6656
0105
32
.33
.1089
.5511
.0359
.2546
.6992
,0119
33
.34
.1156
.5644
.0393
.2662
.7125
.0134
.34
.35
.1225
.5775
.0429
.3817
.7254
.0150
.35
.36
.1296
.5904
.0467
,2955
.7379
.0166
.36
.37
.1369
.6031
.0507
.3094
.7500
.0187
.37
.36
.1444
.6156
.0549
.3235
.7617
.0209
.38
.39
.1521
.6279
.0593
.3377
.7730
.0231
.39
.40
.1600
.6400
.0640
.3520
.7840
.0256
40
.41
.1661
.6519
.0689
.3665
.7946
.0263
.41
.42
.1764
.6636
.0741
.3810
.8049
.0311
.42
.43
.1849
.6751
.0795
.3957
.6146
0342
.43
.44
.1936
.6864
.0652
.4104
8244
.0375
,44
.45
.2025
.6975
,0911
.4252
.6336
.0410
.45
.46
.2116
.7064
.0973
.4401
6425
,0446
46
.47
.2209
.7191
.1036
.4551
.6511
.0468
.47
.46
.2304
.7296
,1106
.4700
.8594
.0531
.48
.49
.2401
.7399
.1176
.4650
.6673
.0576
.49
.50
.2500
.7500
.1250
,5000
.8750
.0625
.50
U.S. Army Corps of Engineers
A-ll
IM 5-858-6
TABLE A-2. (CONTINUED)
p
n = 4
r = 3
n = 4
r = 2
n = 4
r = 1
n = 5
r ~ 5
n = 5
r = 4
n = 5
r = 3
P
.01
.0000
.0006
.0394
.0000
.0000
.0000
.01
.02
.0000
.0023
.0776
.0000
.0000
.0001
.03
.03
.0001
.0052
.1147
.0000
.0000
.0003
.03
.04
.0002
.0091
.1507
.0000
.0000
.0006
.04
.05
.0005
.0140
.1855
.0000
.0000
.0012
.05
.06
.0008
.0199
.2193
.0000
.0001
.0020
.06
.07
.0013
.0267
.2519
.0000
.0001
.0031
.07
.08
.0019
.0344
.2836
.0000
.0002
.0045
.08
.09
.0027
.0430
.3143
.0000
.0003
.0063
.09
.10
.0037
.0523
.3439
.0000
.0005
.0086
.10
.11
.0049
.0624
.3726
.0000
.0007
.0112
.11
.12
.0063
.0732
.4003
.0000
.0009
.0143
.12
.13
.0079
.0847
.4271
.0000
.0013
.0179
.13
.14
.0098
.0968
.4530
.0001
.0017
.0220
.14
.15
.0120
.1095
.4780
.0001
.0022
.0266
.15
.16
.0144
.1226
.5021
.0001
.0029
.0316
.16
.17
.0171
.1366
.5254
.0001
.0036
.0375
.17
.18
.0202
.1509
.5479
.0002
.0045
.0437
.16
.19
.0235
.1656
.5695
.0002
.0055
.0505
.19
.20
.0272
.1806
.5904
.0003
.0067
.0579
.20
.21
.0312
.1963
.6105
.0004
.0061
.0659
.21
.22
.0356
.3122
.6296
.0005
.0097
.0744
.22
.23
.0403
.2285
.6485
.0006
.0114
.0636
.23
.24
.0453
.2450
.6664
.0008
.0134
.0933
.24
.25
.0506
.2617
.6636
.0010
.0156
.1035
.25
.26
.0566
.3787
.7001
.0012
.0161
.1143
.26
.27
.0628
.2959
.7160
.0014
.0208
.1257
.27
.26
.0694
.3132
.7313
.0017
.0236
.1376
.28
.29
.0763
.3307
.7459
.0021
.0272
.1501
.29
.30
.0837
.3483
.7599
.0024
.0308
.1631
.30
.31
.0915
.3660
.7733
.0029
.0347
.1766
.31
.32
.0996
.3837
.7862
.0034
.0390
.1905
.32
.33
.1082
.4015
.7985
.0039
.0436
.2050
.33
.34
.1171
.4193
.6103
.0045
.0466
.2199
.34
.35
.1265
.4370
.8215
.0053
.0540
.2352
.35
.36
.1362
.4547
.8322
.0060
.0596
.2509
.36
.37
.1464
.4724
.8425
.0069
.0660
.2670
.37
.38
.1569
.4900
.8522
.0079
.0726
.2835
.38
.39
.1679
.5075
.8615
.0090
.0796
.3003
.39
.40
.1792
.5246
.8704
.0102
.0870
.3174
.40
.41
.1909
.5420
.8788
.0116
.0949
.3349
.41
.42
.2030
.5590
.8868
.0131
.1033
.3525
.42
.43
.2155
.5759
.8944
.0147
.1121
.3705
.43
.44
.2283
.5926
.9017
.0165
.1214
.3866
.44
.45
.2415
.6090
.9085
.0185
.1312
.4069
.45
.46
.2550
.6252
.9150
.0206
.1415
.4253
.46
.47
.2689
.6412
.9211
.0229
.1522
.4439
.47
.48
.2831
.6569
.9269
.0255
.1635
.4625
.4d
.49
.2977
.6724
.9323
.0262
.1752
.4613
.49
.50
.3125
.6875
.9375
.0313
.1875
.5000
.50
A-12
TABLE A-2. (CONTINUED)
TM 5-858-6
p
n = 5
r = 2
n = 5
r = 1
n = 6
r = 6
n = 6
r 5
n = 6
r = 4
n = 6
r = 3
P
.01
.0010
.0490
.0000
.0000
.0000
.0000
.01
.02
.0038
.0961
.0000
.0000
.0000
.0002
.02
.03
.0085
.1413
.0000
.0000
.0000
.0005
.03
.04
.0148
.1846
.0000
.0000
0000
.0012
.04
.05
.0226
.2262
.0000
.0000
.0001
.0022
.05
.06
.0319
.2661
.0000
.0000
.0002
.0038
.06
.07
.0425
.3043
.0000
.0000
.0003
.0058
.07
.08
.0544
.3409
.0000
.0000
.0005
.0085
.08
.09
.0674
.3760
.0000
.0000
.0008
.0118
.09
.10
.0815
.4095
.0000
.0001
.0013
.0159
.10
.11
.0965
.4416
.0000
.0001
.0018
.0206
.11
.12
.1125
.4723
.0000
.0001
.0025
.0261
.12
.13
.1292
.5016
.0000
.0002
.0034
.0324
.13
.14
.1467
.5296
.0000
.0003
.0045
.0395
.14
.15
.1648
.5563
.0000
.0004
.0059
.0473
.15
.16
.1835
.5818
.0000
.0005
.0075
.0560
.16
.17
.2027
.6061
.0000
.0007
.0094
.0655
.17
.18
.2224
.6293
.0000
.0010
.0116
.0759
.18
.19
.2424
.6513
.0000
.0013
.0141
.0870
.19
.20
.2627
.6723
.0001
.0016
.0170
.0989
.20
.21
.2833
.6923
.0001
.0020
.0202
.1115
.21
.22
.3041
.7113
.0001
.0025
.0239
.1250
.22
.23
.3251
.7293
.0001
.0031
.0260
.1391
.23
.24
.3461
.7464
.0002
.0038
,0326
.1539
.24
.25
.3672
.7627
.0002
.0046
.0376
.1694
.25
.26
.3883
.7781
.0003
.0056
.0431
.1856
.26
.27
.4093
.7927
.0004
.0067
.0492
.2023
.27
.28
.4303
.8065
.0005
.0079
.0557
.2196
.28
.29
.4511
.8196
.0006
.0093
.0626
.2374
.29
.30
.4718
.8319
.0007
.0109
.0705
.2557
.30
.31
.4923
.8436
.0009
.0127
.0787
.27a4
.31
.32
.5125
.8546
.0011
.0148
.0875
.2936
.32
.33
.5325
.8650
.0013
.0170
.0969
.3130
.33
.34
.5522
.8748
.0015
.0195
.1069
.3328
.34
.35
.5716
.8840
.0018
.0223
.1174
.3529
.35
.36
.5906
.8926
.0022
.0254
.1286
.3732
.36
.37
.6093
.9008
.0026
.0288
.1404
.3937
.37
.38
.6276
.9084
.0030
.0325
.1527
.4143
.38
.39
.6455
.9155
.0035
.0365
.1657
.4350
.39
.40
.6630
.9222
.0041
.0410
.1792
.4557
.40
.41
.6801
.9285
.0048
.0458
.1933
.4764
.41
.42
.6967
.9344
.0055
.0510
.2080
.4971
.42
.43
.7129
.9398
.0063
.0566
.2232
.5177
.43
.44
.7286
.9449
,0073
.0627
.2390
.5382
.44
.45
.7438
.9497
.0083
.0692
.2553
.5565
.45
.46
.7585
.9541
.0095
.0762
.2721
.5786
.46
.47
.7728
.9582
.0108
.0837
.2893
.5985
.47
.48
.7865
.9620
.0122
.0917
.3070
.6180
.48
.49
.7998
.9655
.0138
.1003
.3252
.6373
.49
.50
.8125
.9687
.0156
.1094
.3437
.6562
.50
A-13
TM 5-858-6
TABLE A-2. (CONTINUED)
p
n = 6
r = 2
n = 6
r = 1
n = 7
r = 7
n = 7
r * 6
n = 7
r = 5
n = 7
r = 4
P
.ot
,0015
.0585
.0000
.0000
.0000
.0000
.01
.02
.0057
.1142
.0000
.0000
.0000
.0000
.02
.03
.0125
.1670
.0000
.0000
.0000
.0000
.03
.04
.0216
.2172
.0000
.0000
.0000
.0001
.04
.05
.0326
.2649
.0000
.0000
.0000
.0002
.05
.06
.0459
.3101
.0000
.0000
.0000
.0004
.06
.07
.0606
.3530
.0000
.0000
.0000
.0007
.07
.OS
.0773
.3936
.0000
.0000
.0001
.0012
.08
.09
.0952
.4321
.0000
.0000
.0001
,0018
.09
10
.2143
.4666
.0000
.0000
.0002
.0027
.10
.11
.1345
.5030
.0000
.0000
.0003
.0039
.11
.12
.1556
.5356
.0000
.0000
.0004
.0054
.12
.13
.1776
.5664
.0000
.0000
.0006
.0072
.13
.14
.2003
.5954
.0000
.0000
.0009
.009a
.14
.15
.2235
.6229
.0000
.0001
.0012
,0121
.15
.16
.2472
.6467
.0000
.0001
.0017
.0153
.16
.IT
.2713
.6731
.0000
,0001
.0022
.0169
.17
.16
.2956
6960
.0000
.0002
.0029
.0231
.16
.19
.3201
.7176
.0000
.0003
.0037
.0279
.19
.20
.3446
.7379
.0000
.0004
.0047
.0333
.20
.21
,3692
.7569
.0000
.0005
.0056
.0394
.21
.22
.3937
.7748
.0000
.0006
.0072
.0461
.22
.23
.4180
.7916
.0000
.0008
.0086
.0536
.23
.24
.4422
.8073
.0000
.0011
.0107
.0617
.24
.25
.4661
.6220
.0001
.0013
.0129
.0706
.25
.26
.4896
.8358
.0001
0017
.0153
.0602
.26
.27
.5126
.8467
.0001
.0021
.0181
.0905
.27
.28
.5356
.6607
.0001
.0026
.0213
.1016
.26
.29
.5560
.6719
.0002
.0031
.0246
.1134
.29
.30
.5798
.8824
.0002
.0038
.0286
.1260
.30
.31
.6012
.8921
.0003
.0046
.0332
.1394
.31
.32
.6220
.9011
.0003
.0055
.0380
.1534
.32
.33
.6422
.9095
.0004
.0065
.0434
.1682
.33
.34
.6619
.9173
.0005
.0077
.0492
.1637
.34
.35
.6609
.9246
.0006
.0090
.0556
.1998
.35
.36
.6994
.9313
.0008
.0105
.0625
.2167
.36
.37
.7172
.9375
.0009
.0123
.0701
.2341
.37
.38
.7343
.9432
.0011
.0142
.0782
.2521
.38
.39
;7508
.9485
.0014
.0164
.0869
.2707
.39
.40
.7667
.9533
.0016
.0188
.0963
.2898
.40
.41
.7819
.9578
.0019
.0216
.1063
.3094
.41
.42
.7965
.9619
.0023
.0246
.1169
.3294
.42
.43
.8105
.9657
.0027
.0279
.1282
.3498
.43
.44
.8236
.9692
.0032
.0316
.1402
.3706
44
.45
.8364
.9723
.0037
.0357
.1529
,3917
.45
.46
.8485
.9752
.0044
.0402
.1663
.4131
.46
.47
.8599
.9778
.0051
.0451
.1603
.4346
.47
.48
.8707
.9802
.0059
.0504
.1951
.4563
.46
.49
.8610
.9824
.0068
.0562
.2105
.4781
.49
.50
.8906
.9844
.0078
.0625
.2266
.5000
.50
I
TABLE A-2. (CONTINUED)
TM 5-858-6
p
n = 7
r = 3
n = 7
r = 2
n = 7
r = 1
n = 8
r * 8
n = 8
r = 7
n = 8
r = 6
P
.01
.0000
.0020
.0679
.0000
0000
.0000
.01
.02
.0003
.0079
.1319
.0000
.0000
.0000
.02
.03
.0009
.0171
.1930
.0000
.0000
.0000
,03
.04
.0020
.0294
.2486
.0000
.0000
.0000
.04
.05
.0038
.0444
.3017
.0000
.0000
.0000
.05
.06
.0063
.0618
.3515
.0000
.0000
.0000
.06
.07
.0097
.0813
.3983
.0000
.0000
.0000
.07
.08
.0140
.1026
.4422
.0000
.0000
.0000
.08
.09
.0193
.1255
.4832
.0000
.0000
.0000
.09
.10
.0257
.1497
.5217
.0000
.0000
.0000
.10
.11
.0331
.1750
.5577
.0000
.0000
.0000
.11
.12
.0416
.2012
.5913
.0000
.0000
.0001
.12
.13
.0513
.2281
.6227
.0000
.0000
.0001
.13
.14
.0620
.2556
.6521
.0000
.0000
.0002
.14
.15
.0738
.2834
.6794
.0000
.0000
.0002
.15
.16
.0866
.3115
.7049
0000
.0000
.0003
.16
.17
.1005
.3396
.7286
.0000
.0000
.0005
.17
.18
.1154
.3677
.7507
.0000
.0000
.0007
.18
.19
.1313
.3956
.7712
.0000
.0001
.0009
.19
.20
.1480
.4233
.7903
.0000
.0001
,0012
.20
.21
.1657
.4506
.8080
.0000
.0001
.0016
.21
.22
.1841
.4775
.8243
.0000
.0002
.0021
.22
.23
.2033
.5040
.8395
.0000
.0002
.0027
.23
.24
.2231
.5298
.6535
.0000
.0003
.0034
.24
.25
.2436
.5551
.8665
.0000
,0004
.0042
.25
.26
.2646
.5796
.8785
.0000
.0005
.0052
.26
.27
.2861
.6035
.8895
.0000
.0006
.0064
.27
.28
.3081
.6266
.8997
.0000
.0008
.0078
.28
.29
.3304
.6490
.9090
.0001
.0010
.0094
.29
.30
.3529
.6706
.9176
.0001
.0013
.0113
.30
.31
.3757
.6914
.9255
.0001
.0016
.0134
.31
32
.3987
.7113
.9328
.0001
.0020
.0159
.32
.33
.4217
.7304
.9394
.0001
,0024
.0187
.33
.34
.4447
.7487
.9454
.0002
,0030
.0218
.34
.35
.4677
.7662
.9510
.0002
.0036
.0253
.35
.36
.4906
.7828
.9560
.0003
.0043
.0293
.36
.37
.5134
.7987
.9606
.0004
.0051
.0336
.37
.38
.5359
.8137
.9648
.0004
.0061
.0385
.38
.39
.5581
.8279
.9686
.0005
.0072
,0439
.39
.40
.5801
.8414
.9720
.0007
.0085
,0498
.40
.41
.6017
.8541
.9751
.0008
.0100
,0563
.41
.42
.6229
.8660
.9779
.0010
.0117
.0634
.42
.43
.6436
.8772
.9805
.0012
.0136
.0711
.43
.44
.6638
.8877
.9827
.0014
.0157
.0794
.44
.45
.6836
.8976
.9848
.0017
.0181
.0865
.45
.46
.7027
.9068
.9866
.0020
.0208
.0982
.46
.47
.7213
.9153
.9883
.0024
.0239
.1066
.47
.48
.7393
.9233
.9897
.0028
.0272
.1198
.48
.49
.7567
.9307
.9910
.0033
.0310
.1318
.49
.50
.7734
.9375
.9922
.0039
.0352
.1445
.50
A- 15
TM 5-858-6
TABLE A- 2. (CONTINUED)
p
n = 8
r = 5
n = 8
r = 4
n = 8
r = 3
n = 8
r = 2
n = 8
r = 1
n = 9
r = 9
p
.01
.0000
.0000
.0001
.0027
.0773
.0000
.01
.02
.0000
.0000
.0004
.0103
.1492
.0000
.02
.03
.0000
.0001
.0013
.0223
.2163
.0000
.03
.04
.0000
.0002
.0031
.0361
.2786
.0000
.04
.05
.0000
.0004
.0058
.0572
.3366
.0000
.05
06
.0000
.0007
.0096
.0792
.3904
.0000
.06
.07
.0001
.0013
.0147
.1035
.4404
.0000
.07
.06
.0001
.0022
.0211
.1298
.4868
.0000
.08
.09
.0003
.0034
.0289
.1577
.5297
.0000
.09
.10
.0004
.0050
.0381
.1869
.5695
.0000
.10
.11
.0007
.0071
.0487
.2171
.6063
.0000
.11
.12
.0010
.0097
.0608
.2460
.6404
.0000
.12
.13
.0015
.0129
.0743
.2794
.6718
.0000
.13
.U
.0021
.0166
.0891
.3111
.7008
.0000
.14
.15
.0029
.0214
.1052
.3426
.7275
.0000
.15
.16
.0038
.0267
.1226
.3744
.7521
.0000
.16
.17
.0050
.0328
.1412
.4057
.7748
.0000
,17
.id
.0065
.0397
.1608
.4366
.7956
.0000
.16
.19
.0063
.0476
.1815
.4670
.8147
.0000
.19
.20
.0104
.0563
.2031
.4967
.8322
.0000
.20
.21
.0129
.0659
.2255
.5257
.8463
.0000
.21
.22
.0158
.0765
.2486
.5538
.8630
.0000
.22
.23
.0191
.0880
.2724
.5611
.8764
.0000
.23
.24
.0230
.1004
.2967
.6075
.8887
.0000
.24
.25
.0273
.1138
.3215
.6329
.8999
.0000
.25
.26
.0322
.1261
.3465
.6573
.9101
.0000
.26
.27
.0377
.1433
.3718
.6807
.9194
.0000
.27
.26
.0436
.1594
.3973
.7031
.9278
.0000
.26
.29
.0505
.1763
.4226
.7244
.9354
.0000
.29
.30
.0560
.1941
.4482
.7447
.9424
.0000
.30
.31
.0661
.2126
.4736
.7640
.9486
.0000
.31
.32
.0750
.2319
.4987
.7822
.9543
.0000
.32
.33
.0646
*2519
.5236
.7994
.9594
.0000
.33
.34
.0949
.2724
.5481
.8156
.9640
.0001
.34
.35
.1061
.2936
.5722
.8309
.9681
.0001
.35
.36
.1160
.3153
.5958
.6452
.9719
.0001
.36
.37
.1307
.3374
.6189
.6586
.9752
.0001
.37
.36
.1443
.3599
.6415
.8711
.9782
.0002
.38
.39
.1566
.3628
.6634
.6828
.9808
.0002
.39
.40
.1737
.4059
.6646
.6936
.9832
.0003
.40
.41
.1895
.4292
.7052
.9037
.9853
.0003
.41
.42
.2062
.4527
.7250
.9130
.9872
.0004
.42
.43
.2235
.4762
.7440
.9216
.9869
.0005
.43
.44
.2416
.4996
.7624
.9295
.9903
.0006
.44
.45
.2604
.5230
.7799
.9366
.9916
.0008
.45
.46
.2798
.5463
.7966
.9435
.9928
.0009
.46
.47
.2999
.5694
.8125
.9496
.9938
.0011
.47
.46
.3205
.5922
.8276
.9552
.9947
.0014
.46
.49
.3416
.6146
.8419
.9602
.9954
.0016
.49
.50
.3633
.6367
.8555
.9646
.9961
.0020
.50
A-16
TABLE A-2. (CONTINUED)
TM 5-858-6
p
n = 9
r = 8
n = 9
r = 7
n = 9
r = 6
n = 9
r = 5
n = 9
r = 4
n = 9
r = 3
P
.01
.0000
.0000
.0000
.0000
.0000
.0001
.01
.02
.0000
.0000
,0000
.0000
.0000
.0006
.02
.03
.0000
.0000
.0000
.0000
.0001
.0020
.03
.04
.0000
.0000
.0000
.0000
.0003
.0045
.04
.05
.0000
.0000
.0000
.0000
.0006
.0084
.05
.06
.0000
.0000
.0000
.0001
.0013
.0138
.06
.07
.0000
.0000
.0000
.0002
.0023
.0209
.07
.08
.0000
.0000
.0000
.0003
.0037
.0298
.08
.09
0000
.0000
.0000
.0005
.0057
.0405
.09
.10
.0000
.0000
.0001
.0009
.0083
.0530
.10
.11
.0000
.0000
.0001
.0014
.0117
.0672
.11
13
.0000
.0000
.0002
.0021
.0158
.0833
.12
.13
.0000
.0000
.0003
.0030
.0209
.1009
.13
.14
.0000
.0000
.0004
.0041
.0269
.1202
.14
.15
.0000
.0000
.0006
.0056
.0339
.1409
.15
.16
.0000
.0001
.0009
.0075
.0420
.1629
.16
.17
.0000
.0001
.0013
.0098
.0512
.1861
.17
.18
.0000
.0002
.0017
.0125
.0615
.2105
.18
.19
.0000
.0002
.0023
.0158
.0730
.2357
.19
.20
.0000
.0003
.0031
.0196
.0856
.2618
.20
.21
.0000
.0004
.0040
.0240
.0994
.2885
.21
.22
.0000
.0006
.0051
.0291
.1144
.3158
.22
.23
.0001
.0008
.0065
.0350
.1304
.3434
.23
.24
.0001
.0010
.0081
.0416
,1475
.3713
.24
.25
.0001
.0013
.0100
.0489
.1657
.3993
.25
.26
.0001
.0017
.0122
.0571
.1849
.4273
.26
.27
.0002
.0022
.0149
.0662
.2050
.4552
.27
.28
.0003
.0028
.0179
.0762
.2260
.4829
.28
.29
.0003
.0035
.0213
.0870
.2478
.5102
.29
.30
,0004
.0043
.0253
.0988
.2703
.5372
.30
.31
.0006
.0053
.0298
.1115
.2935
.5636
.31
.32
.0007
.0064
.0348
.1252
.3173
.5894
.32
.33
.0009
.0078
.0404
.1398
.3415
.6146
.33
.34
.0011
.0094
.0467
.1553
.3662
.6390
.34
.35
.0014
.0112
.0536
.1717
.3911
.6627
.35
.36
.0017
.0133
.0612
.1890
.4163
.6856
.36
.37
.0021
.0157
.0696
.2072
.4416
,7076
.37
.38
.0026
.0184
.0787
.2262
.4669
.7287
.38
.39
.0031
.0215
.0886
.2460
.4922
.7489
.39
.40
.0038
.0250
.0994
.2666
.5174
.7682
.40
.41
.0046
.0290
.1109
.2878
.5424
.7866
.41
.42
.0055
.0334
.1233
.3097
.5670
.8039
.42
.43
.0065
.0383
.1366
.3322
.5913
.8204
.43
.44
.0077
.0437
.1508
.3551
.6152
.8359
.44
.45
.0091
.0498
.1658
.3786
.6386
.8505
.45
.46
.0107
0564
.1817
.4024
.6614
.8642
.46
.47
.0125
.0637
.1985
.4265
.6836
.8769
.47
.48
.0145
.0717
.2161
.4509
.7052
.8889
.48
49
.0169
.0804
.2346
.4754
.7260
.8999
.49
.50
.0195
.0898
.2539
.5000
.7461
.9102
.50
A-17
TM 5-858-6
TABLE A-2. (CONTINUED)
p
n = 9
r = 2
n = 9
r = 1
n = 10
r = 10
n = 10
r = 9
n = 10
r = 8
n = 10
r = 7
P
.01
.0034
.0665
.0000
.0000
.0000
.0000
.01
.02
.0131
.1663
.0000
.0000
.0000
.0000
.02
.03
.0262
.2398
.0000
.0000
.0000
.0000
.03
.04
.0478
.3075
.0000
.0000
.0000
.0000
.04
.05
.0712
.3698
.0000
.0000
.0000
.0000
.05
.06
.0978
.4270
.0000
.0000
.0000
.0000
.06
.07
.1271
.4796
.0000
.0000
.0000
.0000
,07
.08
.1583
.5278
.0000
.0000
.0000
.0000
.08
.09
.1912
.5721
.0000
.0000
.0000
,0000
.09
.10
.2252
.6126
.0000
.0000
.0000
,0000
.10
.11
.2599
.6496
.0000
.0000
.0000
.0000
.11
.12
.2951
.6635
.0000
.0000
.0000
.0000
.12
.13
.3304
.7145
.0000
.0000
.0000
,0001
.13
.14
.3657
.7427
.0000
.0000
.0000
,0001
.14
.15
.4005
.7684
.0000
.0000
.0000
.0001
.15
.16
4346
.7916
.0000
.0000
.0000
,0002
.16
.17
.4665
.6131
.0000
.0000
.0000
,0003
.17
.16
.5012
.6324
.0000
.0000
.0000
.0004
.18
.19
.5330
.8499
.0000
.0000
.0001
.0006
.19
.20
.5636
.8658
.0000
.0000
.0001
.0009
.20
.21
.5934
.8801
.0000
.0000
.0001
.0012
.21
.22
.6216
.8931
.0000
.0000
.0002
.0016
.22
.23
.6491
.9046
.0000
.0000
.0002
,0021
.23
.24
.6750
.9154
.0000
.0000
.0003
,0027
.24
.25
.6997
.9249
.0000
.0000
.0004
,0035
.25
.26
.7230
.9335
.0000
.0000
.0006
,0045
.26
.27
.7452
.9411
.0000
.0001
.0007
.0056
.27
.26
.7660
.9480
.0000
.0001
.0010
.0070
.26
.29
.7656
.9542
.0000
.0001
.0012
.0087
.29
.30
.6040
.9596
.0000
.0001
.0016
.0106
.30
31
8212
.9645
.0000
.0002
.0020
.0129
.31
.32
.6372
.9669
.0000
.0003
.0025
.0155
.32
.33
.6522
.9728
.0000
.0003
.0032
.0165
.33
.34
.8661
.9762
.0000
.0004
.0039
.0220
.34
.35
.8789
.9793
.0000
.0005
.0048
.0260
.35
.36
.8906
.9620
.0000
.0007
.0059
.0305
.36
.37
.9017
9844
.0000
.0009
.0071
.0356
.37
.36
,9116
.9865
.0001
.0011
.0066
.0413
.38
.39
.9210
.9663
.0001
.0014
.0103
.0477
.39
.40
.9295
.9899
.0001
.0017
.0123
,0548
.40
.41
.9372
.9913
.0001
.0021
.0146
.0626
.41
.42
,9442
.9926
.0002
.0025
.0172
.0712
.42
.43
.9505
.9936
.0002
.0031
.0202
.0806
.43
.44
.9563
.9946
.0003
.0037
.0236
.0908
.44
.45
.9615
.9954
.0003
.0045
.0274
.1020
.45
.46
.9662
.9961
.0004
.0054
.0317
.1141
.46
.47
.9704
.9967
.0005
.0065
.0366
.1271
.47
.46
.9741
.9972
.0006
.0077
.0420
.1410
.48
.49
.9775
.9977
.0008
.0091
.0480
.1560
.49
.50
.9605
.9960
.0010
.0107
.0547
.1719
.50
A-18
TABLE A-2. (CONCLUDED)
TM 5-858-6
p
n = 10
r = 6
n = 10
r = 5
n = 10
r = 4
n = 10
r = 3
n = 10
r = 2
n = 10
r = 1
P
.01
.0000
.0000
.0000
.0001
.0043
.0956
.01
.02
.0000
.0000
.0000
.0009
.0162
.1829
.02
03
.0000
.0000
.0001
.0028
.0345
.2626
.03
04
.0000
.0000
.0004
.0062
.0582
.3352
.04
.05
.0000
.0001
.0010
.0115
.0661
.4013
.05
06
.0000
.0002
.0020
.0188
.1176
.4614
.06
07
.0000
.0003
.0036
.0283
.1517
.5160
.07
08
.0000
.0006
.0058
.0401
.1879
.5656
.08
.09
.0001
.0010
.0088
.0540
.2254
.6106
.09
.10
.0001
.0016
.0128
.0702
.2639
.6513
.10
11
.0003
.0025
.0178
.0884
.3028
.6882
.11
.12
.0004
.0037
.0239
.1087
.3417
.7215
.12
13
.0006
.0053
.0313
.1308
.3804
.7516
.13
.14
.0010
.0073
.0400
.1545
.4184
.7787
.14
.15
.0014
.0099
.0500
.1798
.4557
.8031
.15
.16
.0020
.0130
.0614
.2064
.4920
.8251
.16
.17
.0027
.0168
.0741
.2341
.5270
.8448
.17
.16
.0037
.0213
.0883
.2628
.5608
.8626
.16
19
.0049
.0266
.1039
.2922
.5932
.8784
.19
20
.0064
.0328
.1209
.3222
.6242
.8926
.20
21
.0082
.0399
.1391
.3526
.6536
.9053
.21
22
.0104
.0479
.1587
.3831
.6815
.9166
.22
23
.0130
.0569
.1794
.4137
.7079
.9267
.23
24
.0161
.0670
.2012
.4442
.7327
.9357
.24
25
.0197
.0781
.2241
.4744
.7560
.9437
.25
26
.0239
.0904
.2479
.5042
.7778
.9508
.26
.27
.0287
.1037
.2726
.5335
.7981
.9570
.27
.28
.0342
.1181
.2979
.5622
.8170
.9626
.28
.29
.0404
.1337
.3239
.5901
.8345
.9674
.29
.30
.0473
.1503
.3504
.6172
.8507
.9718
.30
.31
.0551
.1679
.3772
.6434
.8656
.9755
.31
.32
.0637
.1867
.4044
.6687
.8794
.9789
.32
.33
.0732
.2064
.4316
.6930
.8920
.9818
.33
.34
.0836
.2270
.4589
.7162
.9035
.9843
.34
.35
.0949
.2485
.4862
.7384
.9140
.9865
.35
.36
.1072
.2708
.5132
.7595
.9236
.9885
.36
.37
.1205
.2939
.5400
.7794
.9323
.9902
.37
.38
.1348
.3177
.5664
.7983
.9402
.9916
.38
39
.1500
.3420
.5923
.8160
.9473
.9929
.39
40
.1662
.3669
.6177
.8327
.9536
.9940
.40
41
.1834
3922
.6425
.8483
.9594
.9949
.41
42
.2016
.4178
.6665
.8628
.9645
.9957
.42
.43
.2207
.4436
.6898
.8764
.9691
.9964
.43
44
.2407
.4696
.7123
.8889
.9731
.9970
.44
45
.2616
.4956
.7340
.9004
.9767
.9975
.45
46
.2832
.5216
.7547
.9111
.9799
.9979
.46
47
.3057
.5474
.7745
.9209
.9827
.9983
.47
48
.3288
.5730
.7933
.9298
.9652
.9986
.48
49
.3526
.5982
.8112
.9379
.9874
.9988
*49
50
.3770
.6230
.8281
.9453
.9893
.9990
.50
A-19
B
FR
B-l. Simulofioii techniques.
a. The catalog of techniques that follows was
compiled primarily from two sources. "Nuclear
Blast and Shock Simulators," a report
(GE-TEMPO, 1972) by Panel N-2 of the Tripartite
Technical Cooperation Programme (whose member
nations are the United States, Canada, and the
United Kingdom), contains descriptions of tests
from which summaries have been tabulated herein.
The second source was Rowan (1974) which tab-
ulates other items besides airblast and ground mo-
tion that are common to the TTCP report. Specifi-
cally, there are sections relating to simulation of
nuclear radiation, spallation impulse, thermal radi-
ation, EMP, and debris. While a bit dated in some
cases, it is still a worthwhile compilation from
which future work may proceed. Additional re-
ferences are listed in the bibliography, appendix D,
grouped into categories pertinent to testing for nu-
clear weapon effects.
6. An extensive catalog of techniques is presented
in tables B-l through B-10. Recommended test con-
cepts range from laboratory and simple in-plant
tests to numberous field tests that can stimulate
all or portions of the nuclear environment exper-
ienced by major components and subsystems of a
facility. Laboratory and in plant test concepts.
However, experience with field tests is limited; the
cost of field tests will generally be high.
c. The important test comcepts considered are as
follows:
High-Explosive Simulation Technique
(HEST)
Direct-Induced High-Explosive Simulation
Technique (DIEHEST)
High-Explosive Contact Surface Burst
Underground Nuclear Tamped Burst
Underground Nuclear Tunnel Test
Giant Reusable Air-Blast Simulator
(GRABS)
EMP Simulation Testing
Blast Simulation Technique for Testing Air
Entrainment Systems and Blast
Closures.
The following subsections discuss these critical test
concepts in greater detail than is possible in the
catalog presented as tables. More detailed evalu-
ation and development of each of these test con-
cepts is necessary in order to select the appropriate
hardness verification test procedures for a pos-
tulated nuclear burst.
B-2. High-explosive simulation
technique
a. The HEST concept has been used four times
for tests on operational Minuteman sites. The tech-
nique had been expanded for high-overpressure
tests in a rock medium. Periodically, variations of
the HEST test are utilized for special applications.
The reader is urged to review the current literature
to determine whether recent tests have relevance
to his application. A summary of HEST experi-
ments from 1964 to 1974 is listed in table B-ll.
6. The objective of the technique is to simulate
the overpressure and superseismic air-induced
ground shock from a nuclear detonation
Operational and small scale tests have
demonstrated the feasibility of simulating over-
pressures (for about the first 200 msec) from yields
up to 10 Mt and for overpressures up to 3000 psi.
c. HEST uses a confined detonation of explosive
fuse (Primacord) to produce a pressure pulse de-
signed to travel over the ground surface at the
same velocity as an air shock wave of equal inten-
sity, and to have a timedecay shape similar to the
early part of the pressure pulse produced by a
nuclear detonation. A HEST facility consists of a
platform structure constructed above the surface of
the ground over the installation to be tested. (See
figure 4-1 for facility configuaration.) The platform
supports an overburden of earth and forms a cavity
between the bottom of the overburden and the
ground. An earthen embankment is built around
the perimeter of the platform. Primacord is
wrapped on wooden racks that are suspended in
the cavity. Since Primacord detonates at a velocity
greater than the shock front velocity to be simu-
lated, the cord is wrapped at an angle to the direc-
tion of propagation. The intensity of the pressure
pulse depends primarily on the loading density
(amount of explosives per unit cavity volume). The
overburden placed over the HEST platform is com-
pressed and accelerated upward when the overpres-
sure acts on its base, and this upward motion of
the overburden causes the volume of the cavity to
expand, with a corresponding decrease in pressure.
d. Operational HEST tests have used a cavity
that is normally 300 ft. sq. For HEST III the
cavity was 5.5 ft deep and the overburden was
about 10 ft thick. Primacord charge density was
0.070 Ib of explosive per cubic foot of cavity, and
the Primacord weave angle was 8 deg 27 min.
B-l
TM 5-858-6
Table B-l. Dynamic Pressure Tests Using Shock Tubes to Simulate Airblast Effect
TABLE B-l. DYNAMIC PRESSURE TESTS USING SHOCK TUBES TO SIMULATE
AIRBLAST EFFECT
FACILITY
EQUIPMENT
PERFORMANCE
TYPE OF TESTS
TYPE AND FORM
OF RESULTS
DASACON
Conical high-
Test section 7.5. ft
Air-blast loading
Time dependent
U.S. Naval Wea-
explosive-driven
x 10 ft dia., 5.5 bar
on full-scale and
measurements of:
pons Laboratory
shock tube.
(80 psi), 300 ins.
small models. For
Overpressure
Dahlgren, VA
Probably the
model sections of
Dynamic Pressure
world's largest
(2455 ft long).
Test section 9 ft
x 15 ft dia., 2.7 bar
(40 psi), 500 ms.
10-ft dia. and
below, altitude
simulation up to
10 5 ft is available.
Acceleration
Velocity/
Displacement
Strain
Video camera and
Test section 12 ft
recorder.
x 22 ft dia., 1.4 bar
(20 psi) , 500 ms.
The above results
are available as
analog or
magnetic 'tape.
High-speed
cine camera film
(up to 10,000
fps).
URS Shock Tunnel
Rectangular ex-
Test section 8.5 ft
Frontal air-blast
Time dependent
San Francisco,
plosively-driven
by 12 ft dia., 40 ft
loading on struc-
measurements of:
CA
reinforced con-
long. Overpressure
tural elements.
Overpressure
crete shock tube.
range 0.1 to 0.75 bar
Dynamic Pressure
Expansion
(1.5 to 11 psi) .
chamber 8.5 ft
Duration range:
Results on
x 12 ft x 92 ft
80 to 50 ms.
magnetic tape
long.
and high-speed
Driver chamber
cine cameras 1000
8.5 ft x 8 ft x
fps color, 2000
63 ft
fps black and
white.
BRL, Aberdeen
Proving Ground,
MD
84ft x 500 ft
total length
Compressed air-
driven dual shock
Test section 8 ft dia.
No target fixing
facilities each
target to be secured
Air-blast loading
on full-scale and
small models.
Simultaneous
Time dependent
measurements of:
Overpressure
Dynamic Pressure
tube. Can be use
to test section walls.
internal blast
either (a) as a
Overpressure range:
loading from in-
separate shock
0.3 to 1.8 bars
let to outlet of
tube or (b) with
(3 to 26 psi) .
air breathing en-
the expansion
chamber joined to
1 sec approx.
gines
the 5.5 ft dia.
shock tube (see
No high-speed
cine facilities.
below), joined
through a large
air breathing en-
gine as a dual
shock tube to
test the behavior
of such engines
under shock
loading.
BRL, Aberdeen
5.5-ft-dia.x 610ft
Test section 5.5 ft
As above.
As above.
Proving Ground,
air-driven shock
dia. Remaining
MD
tube. Driven gas
details as for the
can be heated to
8 ft dia. tubes.
eliminate density
change on expan-
sion of driven
air.
U.S. Army Corps of Engineers
B-2
TM 5-858-6
TABLE B-l. (CONTINUED)
FACILITY
EQUIPMENT
PERFORMANCE
TYPE OF TESTS
TYPE AND FORM
OF RESULTS
AFWL
6 ft dia. x 245 ft
Test section flat
Ground shock and
As above.
Kirtland AFB,
cylindrical high-
platform 5 ft x 8 ft
related studies.
MM
explosive-driven
with 4.5 ft headroom.
Air-blast loading.
shock tube.
Overpressure range
up to 7 bars (100 psi) ,
Duration: 100 to 200
ms.
Sandia Labs
19-ft-dia. high-
Test section 66 ft x
Large military
Time-dependent
Albuquerque,
explosive-driven
19 ft dia. Initial
units at large
measurements of:
NM
blast tunnel.
pressure in the test
angles of attack.
Overpressure
6 ft dia. x 50 ft
section can be varied
Dynamic Pressure
driver.
from 1 psia to 12
Stagnation Press,
6 ft x 150 ft
psia. At 12 psia,
Acceleration
expansion. 40 ft
static overpressure
Displacement
divergent section.
varies between 1 to
Strain
19 ft dia. x 66 ft
6 bars (14 to 87 psi).
Velocity
expansion section.
Duration: 25 to
Results on
50 ms.
magnetic tape.
High-speed cine
camera film up to
8,000 fps.
Sandia Labs
Albuquerque,
6-ft-dia. x 200-
ft high explosive-
Test section 6-ft dia.,
target suspended by
Small military
structures
As for the
19 ft dia.
NM
driven shock
straps, released
tube.
just before shock wave
arrival, and loaded in
free fall. Test sec-
tion ambient pres-
sures from 0.013 bar
(0.2 psia). At ambient
of 0.8 bars, overpres-
sure range is 6 to 14
bars (87 to 200 psi).
Duration: ^ 6 ms.
6-ft-dia. x 50-
Test section 6-ft-
As above.
As for 19 ft dia.
ft-high-explosive-
dia. Target ac-
driven shock
commodation as for
tube. Expendable
200-ft tube above.
driven section.
Test section am-
bient pressure, 0.07
bar, overpressure
10 bars (145 psi) .
Duration: 2 to 8 ms.
Lovelace DNA
Cylindrical com-
Test section (s) 65 ft
Effect of long-
Time dependent
Kirtland AFB,
pressed-air-driv-
by 3.5 ft dia. Over-
duration airblast
measurements of:
Albuquerque,
en shock tube.
pressure: to 2.3 bars
on a variety of
Overpressure
NM
3.5 ft x 15 ft
(0 to 33 psi) . Duration
large animal
Dynamic Pressure
compression
100 ms on end plate
species.
Photography
chamber, 3.5 ft
terminating the tube.
Oscillograph and
x 125 ft exp.
Chart Recorders
chamber. 6 ft
x 30 ft exp.
chamber. 9 ft
long coupling
sect.
B-3
TM 5-858-6
TABLE B-l. (CONCLUDED)
FACILITY
EQUIPMENT
PERFORMANCE
TYPE OF TESTS
TYPE AND FORM
OF RESULTS
ORES
Ralston,
Alberta, Canada
6-ft-dia. high-
explosive-driven
shock tube.
Driven from RDX/
TNT in a gun bar-
rel, or Primacord
line or grid
charge at entrance
to expansion
chamber.
16 in. naval gun
with 165 in. long x
6 ft dia. expans.
chamber. 57 ft x
16 in. permits re-
coilless operation.
Test sections all
6 ft dia.
Overpressure: 0.1 to
2.4 bars (1.4 to 35
psi). Duration: 50
to 70 ms.
Blast loading.
A. High pressure
structural response
studies.
B. Soil medium
studies.
C. Tests on mili-
tary equipment and
material .
D. Tests on targets
in normal reflection
mode.
Time dependent
measurements of:
Overpressure
Dynamic Pressure
Acceleration
Velocity
Displacement
Strain
High-Speed Cine
(20,000 fps)
17-in.
Shadowgraph
Video camera
and Recorder
ORES
Ralston,
Alberta, Canada
3~ft-dia. com-
pressed-air or
high- explosive-
driven shock tube.
Driver section
similar to 6 ft
dia. model, but
uses a 14- in
naval canon barrel
Approx 175 ft.
Test section 6 f t x
3-ft dia.
Compressed Air Driven.
Tests on military
equipment and
material and
dynamic loading
effects.
Time dependent
measurements of:
Overpressure
Dynamic Pressure
Acceleration
Velocity
Displacement
Strain
High-Speed Cine
(20,000 fps)
17 in. Shadowgraph
Video camera
and Recorder
Overpressure 0.5 to
1.0 bars
(2 to 14 psi) .
Duration: 200 ms.
RDX7TNT Driven. Over-
pressure 1.1 to 7.0
bars CIS to 100 psi).
Duration: 50 to 100 ms.
AFWL
Kirtland AFB,
Albuquerque, NM
13-in. dia. driven
by explosive hy-
drogen and oxygen
gas mixture;
Approx 220 ft over
all length.
Test section approx 2 ft
x 13-in. dia.
Overpressure range
3.5 to 45 bars (50 to
650 psi) . Duration:
1 to 4 ms.
High-pressure
tests of Air Force
targets .
Pressure-Time
oscillographs
BRL
Aberdeen Proving
Ground, MD
8 -in. dia. detona-
tion-driven shock
tube. Hydro gen -
oxygen driver
mixture.
Test section 55 ft x
22 -in. dia. Over-
pressure 14 bars
(200 psi) . Duration:
50 ms.
High-pressure
loading.
Oscillographs,
chart, and tape
recorders.
Boeing/SAMSO,
Boeing Tulalip
Test Site,
Tulalip, Wash.
24 in. , 36 in. , and
30 in. x 52 in.
tubes of undeter-
mined length
No data at hand.
--
NOL
Silver Springs,
Maryland
Conical shock
tube.
16-in. dia. test
section at 75 ft;
24-in. dia. test
section at 135 ft.
--
B-4
TM 5-858-6
Table B-2. Ground Shock Using Blast Load Generators to Simulate Airblast Effect
TABLE B-2. GROUND SHOCK USING BLAST LOAD GENERATORS TO SIMULATE
AIRBLAST EFFECT
FACILITY
EQUIPMENT
PERFORMANCE
TYPE OP TESTS
TYPE AND FORM
OF RESULTS
WES
Large blast
Soil loading test
Tests for studies
Time dependent
Vicksburg, MS
load generator
section surface area
in the design and
measurements of:
(LBLG) .
410 ft 3 . Maximum
analysis of under-
Overpressure
available depth of
ground structures.
Soil Stress
burial 10 ft. Pres-
Acceleration
sure to 70 bars
Velocity
(10DO psi) . Dura-
Displacement
tion: to 2 sec.
Str.iin
Magnetic Tape
Records.
4-ft dia.
Static pressures
Testing small
As above.
blast load
up to 135 bars (2000
buried structures,
generator.
psi) of compressed
stress wave prop-
air or water.
agation, and soil
Dynamic pressures
structure
to 17 bars (250 psi) .
interaction.
Durations: to 2 sec.
Static loading
Static pressure to
Static loading of
Static measure-
device.
410 bars (6000 psi) .
buried model
ments of:
structures,
Fluid Pressure
structural ele-
Soil Stress
ments, and sub-
Displacement
merged objects.
and Strain
Waterways Exper-
Vertical
Peak pressures 55 to
Shot duration
Time- dependent
imental Station
detonatable gas
105 bars (800 to 1500
pressure pulses on
measurements of:
Vicksburg, MS
shock tube .
psi) . Durations 3 to
buried model struc-
Pressure
6 ms. Test Cham-
tures and structural
Soil Stress
bers: 46.7 in. dia.
elements.
Acceleration
Depth: (a) 1.75 ft.
Strain
(b) 4 ft.
Magnetic Tape
(c) 5.75 ft.
Records.
NCEL
Blast simu-
Test pit: 9 ft wide x
Static and dynamic
Time-dependent
Port Hueneme,
lator, Primacord
10 ft long x 12 ft
loads on structural
measurements of:
CA
driven.
deep. Peak Pressures:
elements such as
Pressure and
2 to 14 bars (30 to
beams, slabs, and
Strain
200 psi).
model elements.
Oscillograph
Duration: 0.4 to 7.0
Records.
sec.
AFWL
2-ft-dia.
Test pit: 4 ft deep x
Instrumentation
Time-dependent
Kirtland AFB
(0.6 m) high-
2 ft dia. Surface
development, proof,
measurements of:
Albuquerque, NM
explosive-driven
loading. Peak Over-
and testing
Soil
vertical shock
pressure 0.35 to 35
Pressure
tubes.
bars (5 to 500 psi) .
Duration: 30 ms.
GRABS
Explosive cavity
18-ft-dia. x 48-ft-
Buried systems or
See
Air Force Weap-
above soil sample
deep silo, soil test
models of systems,
for discussion
ons Laboratory
in large
bed up to 30 ft of
and soil/structure
of GRABS
Kirtland AFB,
reinforced
depth possible.
interactions.
technique.
NM
concrete- lined
Up -to 1800 psi over-
silo.
pressure possible.
U.S. Army Corps of Engineers
B-5
TM 5-858-6
Table B-3. Dynamic Loading of Material Using Special Test Machines to Simulate Airblast Effect
TABLE B-3. DYNAMIC LOADING OF MATERIAL USING SPECIAL TEST MACHINES
TO SIMULATE AIRBLAST EFFECT
FACILITY
EQUIPMENT
PERFORMANCE
TYPE OF TESTS
TYPE AND FORM
OF RESULTS
Wyle Laboratories
Norco, Calif.
Parallel Pendulum
Impact .
Velocity peak
400 in. /sec.
Shock testing
pieces of equipment
or of shock-
mounted systems
Hammer
shock machine
Velocity peak
200 in. /sec.
As above.
--
Kirtland AFB
Albuquerque , NM
HYGE shock
tester
200 g max :
Duration: 10-50 ms.
Peak force: 47,000 Ib
Wave shape: 1/2 sine
square, triangle
As above.
Anywhere
Quick-release
twang test, from
small lab tests
to full-scale
simulation
Simulates motion
by displacement of
platform rather than
supports .
Shock-isolated
platform evaluation
tests.
Very effective when
properly conducted.
WES
Vicksburg, MS
500-kip ram
loader.
Hydraulic actuator,
pump, and control
system can apply
loads in excess of
350,000 Ib with
approx 1/4- in move-
ment and 80 ms rise-
time.
Applies loads to
construction mate-
rials and struc-
tural elements
where it is neces-
sary to achieve
slowly applied
cyclic or random
loads.
Time -dependent
measurements of:
Load
Strain
Acceleration.
Velocity
Displacement
d.c. to 40 kHz FM
magnetic recorder!
200-kip dynamic
ram loader.
Hydraulic ram
applies 10,000 to
20,000 Ib in either
tension or compres-
sion, either slowly
or within 2 ms.
Tests structural
elements and de-
termines strength
of materials under
slow static or
dynamic loads.
Time- dependent
measurements of:
Load
Strain
Acceleration
Velocity
Displacement
d.c. to 40 kHz FM
magnetic record-
ing
NCEL,
Port Hueneme, CA
50-kip ram
loader.
Max force: 50,000 Ib.
Rise time: 2 to
200 ms. Duration:
to 2 sec. Head
velocity: 3 to 1800
in./min.
Dynamic testing of
metal, concrete,
and other mate-
rial specimens.
Time -dependent
measurements of:
Head displace-
ment
Strain
Head resistance
d.c. to kHz FM
magnetic recording
AFWL
Albuquerque, NM
50-kip ram
loader.
Pneumatic-hydraulic
driver, 100 to 50,000
Ib. Nominal 59,000-
Ib maximum. Rise
time: 1.5 to 50 ms.
Duration: 20 ms to
30 sec. Velocity: 4
in./min to 450 in./min
Test section: 14- to
74 -in. wide by 48 in.
Used either force-
time or constant
velocity loader.
Dynamic testing
of properties of
materials.
Refer to AFWL
U.S. Army Corps of Engineers
B-6
TM 5-858-6
TABLE B-3. (CONCLUDED)
FACILITY
EQUIPMENT
PERFORMANCE
TYPE OF TESTS
TYPE AND FORM
OF RESULTS
WES
Dynamic
Compressed- gas
Dynamic testing to
Time-dependent
Vicksburg, MS
triaxial test
verti cal-load
determine shear
measurements of:
apparatus .
generator 10- to
strength of soils.
Top load
5000-lb load, 4-in.
Bottom load
stroke, 10 ms to
Top
.1 sec time to fai lure.
displacement
WES
Dynamic load-
Compressed-gas
To determine re-
Time -dependent
Vicksburg, MS
test systems.
loaders apply con-
sponse of earth
measurements of:
trolled impulse or
materials and soil
Force genera-
static loads 100 to
structure systems
tion
115,000 Ib on test
to high amplitude
Uniaxial strain
specimens up to
impulse loading
Vertical fluid
8-ft wide by 50-in
(nuclear blast
pressures
high.
simulation) .
Displacements
Triaxial chamber
pressures
Vertical load
Vertical and
horizontal
displacements
on triaxial
specimens.
Oscillograph and
analog-tape
recording.
Explosive-
Explosive plane-
Determination of
Time- dependent
test facility.
wave lens system
Hugoniot equations-
measurements of:
applies high pres-
of-state on:
Pressure
sures (600 kb]
Cements
Strain
on up to 6- ft sur-
Epoxies
Time of
faces. Flying plate
Geological
arrival
techniques also
material
High-speed
employed.
Concrete
oscillographs
and magnetic
(Hardened
tape recording
specimens) .
High-speed
cameras .
Waterways Exper-
Compressed-
Gas gun 20 ft x 2-in.
Shock response or
Particle velocit)
iment Station
gas and powder
dia. operated by
Hugoniot data on
time and
Vicksburg, MS
gun facility.
high-pressure helium
geological mate-
pressure time.
or nitrogen. Speci-
rials, grouts, and
men launched into
concretes.
Oscillograph
evacuated tube. Pow-
recording.
der gun: 20 ft x 2.5-
in. dia. Explosive
driving of specimens
up to 8000 ft/sec.
Launch tube evacuated
and detonation pro-
ducts contained.
NCEL
Dynamic
Primacord driver.
Tests of reinforced
Oscillograph
Port Hueneme, CA
slab loader.
Maximum pressure:
concrete slabs.
recording.
300 psi. Maximum
Oscilloscope
force: 1,560,000 Ib.
photography.
Rise, time: 1 to 3
ms . Decay (several
sec).
B-7
TM 5-858-6
Table B-4. Full-Scale Soil Loading Tests ofAirblast Effect During Field Tests
TABLE B-4. FULL-SCALE SOIL LOADING TESTS OF AIRBLAST EFFECT DURING
FIELD TESTS
FACILITY
EQUIPMENT
PERFORMANCE
TYPE OF TESTS
HEST
Air Force Weap-
ons Laboratory
Kirtland AFB,
Primacord laced
around wooden
racks and deton-
Ground surface air
overpressures in
excess of 1000 psi
Actual prototype,
buried systems,
models of systems,
NM
ated in an air
possible. Accom-
and soil/structure
cavity benearth an
modates very large
interaction.
earth overburden.
test structures.
DIHEST
Arrays of explo-
Horizontal longi-
Buried systems in
Air Force Weap-
sives embedded in
tudinal peak parti-
a variety of geo-
ons Laboratory
the ground.
cal velocities of
logical formations.
Kirtland AFB,
nearly 100 fps at a
DIHEST coupled
NM
range of 10 ft possi-
with HEST provides
ble. Accommodates
simulations of
full-size test struc-
air-blast-induced
tures .
and direct-
induced ground
motion.
DELTA
Explosive cavity
30, 000 -psi maximum,
Models of systems,
Civil Engineer-
above or below
13-ft-dia. test sec-
test to failure.
ing Research
test slab inside
tion, 2-day assembly
Facility
reinforced con-
for each test.
Kirtland AFB,
crete cylinder.
NM
ORES Portable
Horizontal layer
30 to 100 psi over-
Portable ground-
Ralston, Alberta
of explosive with
pressure range.
blast simulator
Canada
water overburden
Positive duration,
pla'ces time-
can be placed over
40 ms. Ground
dependent over-
any existing
surface cover is
pressure loads on
buried structure
17.5 x 16 ft.
existing buried
to be tested.
targets .
Blast-Directing
HE arranged in
Cost well below
Test of full-scale
Techniques
vertical flat
similar pressure
equipment.
DRES
plate.
resulting from
Ralston,
hemispherical
Alberta Canada,
trials. 30 to 450
and
psi range. Target
AWRE
dimension should
Foulness,
be smaller than
England
the HE reactangle.
U.S. Army Corps of Engineers
B-8
TM 5-858-6
I
Table B-5. Dynamic Water Wave and Shock Tests, Simulating Airblast o Direct Shock
Table B-6. Blow-Off Response Using Sheet Explosives to Simulate Nuclear Radiation Effect
TABLE B-5. DYNAMIC WATER WAVE AND SHOCK TESTS, SIMULATING AIRBLAST
ON DIRECT SHOCK U.S. Army Corps of Engineers
FACILITY
EQUIPMENT
PERFORMANCE
TYPE OF TESTS
TYPE AND FORM
OF RESULTS
WES
Big black
Basin 1: 150 ft x 250
Underwater explo-
Time-dependent
Vicksburg, MS
river test
ft x 22 ft deep.
sion effects.
measurements of:
facility.
Detonations up to 150 Ib
Pressure
HE.
Surface Displace-
Basin 2: 160 ft x 260
ft x 12 ft deep. Deto-
ment
Bottom Ground
nation up to several
motion
hundred pound HE.
High-Speed
cinephotographs
Basin 3: Trapezoidal
Explosively gen-
up to thousands
with sloping bottom
erated surface
of frames/sec.
550 ft long; 300 ft wide
effects.
at 0.2 ft depth, 150 ft
wide at 12 ft depth.
Lovelace DNA
Water
Basin 220 ft x 150 ft
Biomedical inves-
Time-dependent
Kirtland AFB
shock facility.
at top, 30 ft deep over
tigations of under-
measurements of:
Albuquerque, NM
a 30. ft x 100 ft por-
water blast effects.
Pressure
tion. Upper limit of
Oscillograph
detonations 27 Ib.
Records.
NCEL
Impulse
Basin 94 ft x 92 ft
Effects of water
Cinephotography .
Port Hueneme,
water wave
x 3 ft deep. Com-
waves on model
CA
facility.
pressed-air-driven
waterfront
plunger. Single
structures .
abrupt and omni-
directional motions
of the plunger are
used.
TABLE B-6. BLOW-OFF RESPONSE USING SHEET EXPLOSIVES TO SIMULATE
NUCLEAR RADIATION EFFECT u%s . Army corps of Engineers
FACILITY
EQUIPMENT
PERFORMANCE
TYPE OF TESTS
TYPE AND FORM
OF RESULTS
Any facility
familiar with
HE techniques
Explosive sheet
in contact
with specimen
10 if taps -0.2 ms
(time proportional to
impulse), 100 kb'peak
pressure .
Maximum achievable is
probably less than 10*
taps - 10 7 taps gives
a 200-ms pulse.
Radiation impulse
loads of closures,
exposed structural
elements.
Explosive sheet
over neoprene
foam
3000 taps on up,
2000-2 ms
0.1 to 10 kb
__
--
Light-initiated
explosives (lead
or silver azide)
1/4 sec pulse
Under development-
dangerous to work
with
"
Explosive mesh
5000 taps minimum
1 ms rise time and
2 x 10~ 8 simultaneity
claimed
B-9
TM 5-858-6
Table B-7. Tests of Nuclear Radiation Effects
Table B-8. Tests of Thermal Radiation Effects
TABLE B~7. TESTS OF NUCLEAR RADIATION EFFECTS
EFFECT
TO BE
SIMULATED
SIMULATION
TECHNIQUE
ENVIRONMENT OR
CHARACTERISTIC
COMMENTS REMARKS
AGENCY
TEST SITE
.
9 11
.
Penetration
of
Plasma
Focus
Total 10-10 w/shot 14 mev n
1/2 sec duration *
intervals. Needs development to
Kaman
Nuclear
Neutrons
Device
be portable. Kaman Nuclear has
and
(Zipper)
best capability.
Neutron-
Induced
Fissionable
Fission spectrum probably
Radiation
Plate + N
largest flux
Source
Pulsed
Fission spectrum up to 10 13 n/cm
From 1963 survey Super Kuka
Battelle Memorial
Reactors
and up to 10 7 rad (c)
Minimum of 10 sec irradiation
Institute
50-100 sec pulse
Steady-
Maximum of 6 x 10 15 n/cm 2 sec
To match
State
Reactors
Penetration
Underground
Maximum of 10 s rad(c)/hr more
Minimum of 1/2 hr, question of
AEC, NTS
of Gamma
Gamma
common is 10 6 rad(c)/hr
spectra must be resolved.
Facilities
Facilities
Gamma
500-Curie source irradiation
Numerous facilities and places
Martin Co.,
Irradiation
20 in. spec at 10 6 rads/hr
Baltimore
Facilities
50ti-Curie source irradiation
20 in. spec at 1.3 x 10 5 rads/hr
Permanent
Pulsed
10 15 n/cm 2 (fission) 600 sec
Use internal chambers for
LRL, Super
Neutron
Reactors
irradiation largest Super Kuka
Kuka
Damage
to be operated in 1968.
Transient
Prompt Gamma
Optimum specimen ^size
(Circa 1967)
USAF/AFSWL,
Radiation
Simulator
Length: 50 cm
Kirtland AFB
Effects
Diameter: 50 cm
Electronic
Target Distance: 75 cm
System
Pulse Length: 70 x 10 9 sec
(TREES)
Max 5000-7000 rads/pulse
10 in. rads/sec
TABLE B-8. TESTS OF THERMAL RADIATION EFFECTS
EFFECT
TO BE
SIMULATED
SIMULATION
TECHNIQUE
ENVIRONMENT OR
CHARACTERISTIC
COMMENTS- -REMARKS
AGENCY
TEST SITE
Thermal
Radiation
on Exposed
Elements
Rocket
Engine
Exhaust
Chemical
Can verify subsystem calculations.
Simulation not really representa-
tive in heat/time relations.
Rocket Test
Stands
Thermal
Radiation
on Exposed
Elements
Thermal
Simulator
Thermal Jet 3-5 cal/cm 2 /sec for
10-cm specimen.
Not fully developed; requires
3-5 year development program
small samples;- could provide
repeatable tests.
DASA
Thermal
Radiation
on Exposed
Elements
Nuclear
Explosion
Shock Tube
(NEST)
Proposal-stage attempt to
simulate effects of a surface
nuclear burst including thermal
radiation, 1/4 subscale model.
Thermal radiation is also produced
in this concept. See detailed
write-up on
AEC/DASA, NTS
(Above appraisals circa 1967)
TM 5-858-6
I
Table B-9. Tests ofEMP Effects
TABLE B-9. TESTS OF EMP EFFECTS
EFFECT
TO BE
SIMULATED
SIMULATION
TECHNIQUE
ENVIRONMENT OR
CHARACTERISTIC
COMMENTS- -REMARKS
AGENCY OR
CONTRACTOR
EMP
Miniature
Max E Field: 2.5 x 10 5 V/m
Small-scale component or
US Army, ERDL
E-Field
Freme
Max B Field: 120 Gauss
subsystem testing
Ft. Belvoir, VA
B-Field
Rise Time: 0.1 x 10~ 6 sec
Duration: 5 x 10" 6 sec
Spec Size: 5 ft dia. x 6 ft
long
EMP
Freme
Max E Field: 10 5 V/m
Full-scale samples of subsystem
US Army, ERDL
E-Field
Max B Field: 60 Gauss
Ft. Belvoir, VA
B-Field
(uniform to 10%)
Rise Time: 0.5 x 10 6 sec
Max Spec Size: 50 ft dia. x
60 ft long
EMP
ALECS
Max E Field: 10 4 V/m
Subsystem or scale samples
AFWL, Kirtland
E-Field
Rise Time: 3-10 x 10~ 9 sec
AFB
Duration: 100 x 10 6 sec
EMP
ALECS
Max E Field: 7.5 x 10 4 V/m
Subsystem or scale samples
AFWL/LASL
E-Field
Rise Time: 5-10 x 10" 9 sec
Pulse Width: 150 x 10' 9 sec
EMP
ARES
Pulse Characteristics--
Facility has a working volume
DNA, Kirtland
E-Field
(Advanced
Peak Output Voltage: 45 MV
40 m high, 30 m long, and
AFB
Research
Energy Storage: 50 kJ
40 m wide.
EMP
Field Strength in working
Shielded instrumentation room
Simulator)
Volume: 110 kV/ra
housed beneath the facility.
Pulse Rise Time: 6 x 10~ 9 sec
Duration: 100-500 x 10' 9 sec
EMP
Orange
Pulse Length characteristics--
Small portable unit
AFSWC/SWTVE,
Bank
Longest: 5 00- V sec rise
Component Testing
Kirtland AFB
Generator
750-ysec decay
Shortest: 6-psec rise
100-ysec decay
Variable frequency control
Capacitor discharge
7 kV - 45 kV
20 kA maximum
APSWC/SWTVE,
EMP
Marx
Pulse Length Characteristics--
Small portable unit for
Kirtland AFB
E-Field
Generator
Longest: 500-ysec rise
subsystems and components
(Small)
7SO-psec decay
Lightning
Shortest: 6-Msec rise
Transient
100-psec decay
Research
Variable frequency control
Institute
Gap discharge 1.4 mV - 15 mV
50 kA maximum
E Field 10 3 - 10 4 V/m
EMP
Marx
Pulse Length Characteristics--
Large portable unit can be taken
AFSWC/SWTVE
E-Field
Generator
Longest: 500-sec rise
to sites for full-scale testing.
Kirtland AFB
(Urge)
750-sec decay
and Field Sites
Shortest: 6-sec rise
100-sec decay
Variable frequency control
Ignition discharge
80 - 320 kV
160 kA maximum
EMP
E-Field
Test
H Field - 1 kHz damped
In-plant small samples
Boeing Co.,
H -Field
Generator
since Wave Peaking at 100
Seattle,
Gauss
Washington
E Free Field - 10 kV/m at 2 m
B-11
TM 5-858-6
TABLE B-9. (CONTINUED)
EFFECT
TO BE
SIMULATED
SIMULATION
TECHNIQUE
ENVI RONMENT OR
CHARACTERISTIC
COMMENTS- - REMARKS
AGENCY OR
CONTRACTOR
EMP
SCREEN
Variable, depending on location
In-plant testing, subsystems
Numerous
Rooms +
and contractor
and scaled components to full-
Generators
scale components .
+ Elect.
Test
Equipment
EMP
Synthetic
Measurement of CW transfer
Proposal by TRW full-scale tests
TRW Systems,
Pulse
functions inside an enclosure
at actual sites
Actual Test Site
Diagnosis
when transmitted at the surface
(SPUD)
EMP
HEMP
Pulse Characteristics--
No working; volume section; just
SAFEGUARD
E-Field
Max voltage: 400 kV
2 transition sections each
Communication
Max field: 26 kV/m
68 m long. Junction of sections
Agency,
Rise time: 3 x 10" 9 sec
is 15 m high and 24 m wide.
Fort Huachuca,
AZ
300 x 10' 9 sec
EMP
SIEGE
Working volume is 3m high and
SAFEGUARD
E-Field
(Simulator-
uses the earth f s the lower
Communication
Induced EMP
plate. Multiple drives, using
Agency,
Ground
8 ft transition.
Fort Huachuca,
EMP
Environment)
TEFS
Designed to test a buried system.
AZ
SAFEGUARD
E-Field
(Transport-
able Electro-
Field strength: 50 kV/ra
Rise time: 4 x 10~ 9 sec
vertical downward direction.
Multiple feeds (144) each
Communication
Agency,
magnetic
Decay time constant:
driving 4 transition sections
Portable, can
Field
350 x 10- 9 sec
(576 total)
be erected on
Simulator)
Can illuminate a 40 m x 40 m area
site
EMP
Sandia
Pulse Characteristics-
Facility is 1000 ft long mounted
Sandia Corp . ,
E-Field
Long Wire
Rise time: 10 x 10"" 9 sec
on 40-ft poles. Powered by two
Kirtland AFB
Duration (to 10%): IxlO" 6 sec
20 kV power supplies.
Peak field strength:
= 1000 V/m
at a point 100 ft from wire.
EMP
Martin-
Pulse Characteristics
Facility is 1000 ft long and
Martin-Marietta
E-Field
Marietta
Rise time: variable
46 ft aboveground.
Corp . ,
Long Wire
5 to 30 x 10~ 9 sec
Powered by two 125 kV power
Orlando, FL
Pulse width: variable
supplies.
100 to 700 x 10' 9 sec
Max field strength:
1100 V/m at 100 ft
Pulse repetition frequency:
CCWP
10 pps
ApOUff 1
EMP
E-Field
AroWL
Dipole
(Long Wire)
Rise time: 7 x 10~ 9 sec
Duration: 200 x 10~ 9 sec
Wire is 320 ft long and 45 ft
aboveground. Located adjacent
to an aircraft parking pad at
AronL ,
Kirtland AFB
Field strength:
Kirtland AFB.
300 V/m at 90 m
Repetition rate: 10 pps
EMP
HDL
Pulse Characteristics--
Biconic sections 9 ft dla. x 9 ft
Harry Diamond Labs
E-Field
Biconic
Rise time: 4 x 10~ 9 sec
long. Overall antenna length is
Woodbridge, VA
Zero crossing at decay:
1000 ft mounted 100 ft
900 x lO' 9 sec
aboveground .
Field strength (at 90 m) :
4.5 kV/m
EMP
RES
A flyable (helicopter) Biconic
AFWL, Portable
E-Field
radiator. Horizontal version is
200 ft long, vertical version is
600 ft long. Design is similar
to HDL simulator.
B-12
TM 5-858-6
TABLE B-9. (CONCLUDED)
UI-'FtiCT
TO BE
SIMULATED
SIMULATION
TECHNIQUE
ENVIRONMENT OR
CHARACTERISTIC
COMMENTS- -REMARKS
AGENCY OR
CONTRACTOR
BMP
E-Field
NOL/ITTRI
Hybrid
Uses a vertical conic antenna
Sub-threat-level facility uniform
NOL/ITTRI
Antenna
fringing line (300 ft)
interaction area.
Crystal Lake,
IL
Rise time: 10 x 10~ 9 sec
Decay time: 1-100 x 10~ 6 sec
Field strength: 100 V/m single
shot, 10 V/m at 60 pps.
EMP
Hybrid
Similar to NOL/ITTRI, above but
To be built at Solomons, Maryland
NOL, Solomons, MD
E-l : ield
Antenna
larger and move powerful. Desigr
for Navy use. (comment Circa
criteria include:
1973)
Length: 1300 ft (.fringing line)
Height: 100 ft [conic antenna)
Field strength:
1000 V/m at 300 m
EMP
DELTA
Pulse Characteristics--
Installed on a mountain top at
White Sand
E-Field
Function
Vertical ly polarized
White Sands Missile Range to
Missile Range,
Simulator
Pulse width (at 50% points)
evaluate aircraft in flight.
New Mexico
2 x 10-9 S ec
Field strength: 5 V/m at 5 ms
Beam width: +20 deg.
Debris
CER Filter
Critical component debris test
Used to verify design and
Contractor,
Testing
and Dust
calculations.
In-Plant
Components
Separator
Test
Maximum
Operating
Operation of debris removal
Laboratory test to confirm design
Contractor
Debris
Test
systems under maximum load.
of debris removal system
In-Plant
Load--
Fixture
Debris
Removal
System
Debris
Operational
Selected debris to simulate
Full-scale operational prototype
Contractor plus
Removal
Test to
maximum load.
system may be conducted in con-
OCE, Field
Demonstrate
junction with other closure
Debris
testing.
Removal
System
B-13
TM 5-858-6
Table B-10. Chronology of HEST and DIHEST Tests
TABLE B-10. CHRONOLOGY OF HEST AND DIHEST TESTS
DATE
TEST
LOCATION
PURPOSE
PIT SIZE,
FT
Feb to Aug 1964
Phase I
(Gas Bag)
Kirtland AFB
Experiment with (1) gas mixture/ water overburden and
(2) detonating cord/sand overburden. Selected latter
20 x 40
method.
Dec 1964
Phase II
Kirtland AFB
Determine pressure area and instrument requirements
96 x 150
for a full-scale Minuteman facility, using a quarter-
scale model.
Feb 1965
(HEST-2)
Kirtland AFB
Study parameters controlling the HEST ait-pressure
32 x 36
time histories.
Mar 1965
(HEST-3)
Kirtland AFB
Study parameters controlling the HEST air-pressure
40 x 48
time histories.
May 1965
Phase IIA
Kirtland AFB
Double overpressure, change surcharge containment, and
88 x 100
improve instruments, using same testbed and structures
as for Phase II.
July 1965
Collins
Kirtland AFB
Using facility similar to Phase IIA, include a cavity
40 x 96
Antenna Test
for investigating response of LEB access and air
entrainment systems and antenna.
1965
Parameter
Kirtland AFB
Study parameters controlling the HEST air-pressure
Various
Studies
time histories.
Oct 1965
(HEST-1)
Kirtland AFB
Study parameters controlling the HEST air-pressure
32 x 36
time histories.
Dec 1965
HEST Test I
Warren AFB
OPERATIONAL TEST: Test an operational Minuteman site
302 x 304
(Quick HEST)
Wing V
with launch facilities and a ground test missile on
simulated alert.
Mar 1966
(HEST-6)
McCormack's
Study free field ground motion.
Ranch,
Albuquerque
May 1966
HIP 1
Kirtland AFB
Improve HEST environment.
40 x 60
June 1966
HIP la
Kirtland AFB
Improve HEST environment.
40 X 60
July 1966
HEST Test II
Warren AFB
Wing V
OPERATIONAL TEST: Demonstrate the degree of structural
survivability of facilities and equipment; assess the
304 x 352
hardness .
Sept 1966
HEST Test II
Grand Forks AFB
OPERATIONAL TEST: Substantiate the hardness of test
site to meet design attack threat; obtain data for
302 x 304
extrapolation of Minuteman force hardness; demonstrate
missile launch capability after test.
Dec 1966
Drillhole
McCormack's
Study free field ground motion.
64 x 148
Ranch,
Albuquerque
July 1967
Backfill
McCormack's
Study free field ground motion.
56 x 72
(HEST-4)
Ranch,
Albuquerque
Oct 1967
HEST V
Grand Forks AF
Demonstrate maximum SOR environment; evaluate surcharg
64 x 83
Demonstratio
Wing VI
disposal; evaluate gage placement techniques; provide
planning basis for HEST Test V. Used smaller pit.
Apr 1968
Mini-Can I
Kirtland AFB
Verify design for Prairie Flat overpressure facility
31 x 75
for Project LN320; however, shock wave outran detona-
front and broke detonating cord.
May 1968
Mini-Can II
Kirtland AFB
Using same site as for Mini -Can I, try 1/16-in. aircra
cable support for detonating cord, but also broken by
31 x 75
shock wave.
B-14
TM 5-858-6
TABLE B-10. (CONCLUDED)
DATE
TEST
LXATION
PURPOSE
PIT SIZE,
FT
May 1968
Mini-Can III
Kirtland AFB
Using same site as Mini-Can I and II, try two methods
for protecting detonating cord; one was successful for
protection, but failed to meet requirements for shock
front velocity and impulse.
31 x 75
Sept 1968
HEST Test V
Grand Forks AFB
Wing VI
* OPERATIONAL TEST: Determine structural survivability
and functional capability of launch-essential systems;
obtain data useful for force hardness assessment.
300 x 300
Sept 1968
Prairie Flat
HEST Test
(Proj. LN320)
Suffield Range,
Canada
HEST Test with model structure; obtain free field
motion and structure response data at specific range
and overpressure levels to compare with those produced
by 500-ton Prairie Flat Trial.
104 x 108
Nov 1968
Rocktest I
Albuquerque
Research in nuclear weapons effects and systems develop-
ment, as applicable to structures in hard rock.
160 x 208
1969
DATEX I
Cedar City
DIHEST Development: Provide information on direct-
induced rock stresses for HANDEC I experiment.
May 1969
HANDEC I
Cedar City
Demonstrate Improved simulation of a nuclear blast by
combining a HEST with DIHEST input to ground motion.
40 x 60
Aug 1969
HANDEC II
Cedar City
Follow-on to HANDEC I, with reduced overpressure while
DIHEST was increased nearly 20 times.
60 x 90
Oct 1969
DATEX II
Cedar City
DIHEST Development: First employment of a slurry
explosive as a loading source.
185 x 200
Mar 1970
Rocktest II
Cedar City
Test realistic configurations of Minuteman launch
structures to' survive the HEST-DIHEST environment in
rock, using ten experimental structures.
250 x 400
U.S. Army Corps of Engineers
a In the testing community the validity of the
equipment to produce simulated airblast-induced
ground motions is much debated. The HEST load-
ing is a moving pressure over a bed with finite
width and length. The true nuclear-induced loading
more correctly resembles a line load with a step
pulse behind the front. The fact that the HEST is
loading only a small area creates an outward and
upward motion adjacent to the bed; the true nu-
clear is essentially a one-dimensional motion. This
outward and upward motion in HEST may signifi-
cantly alter the vertical component of motion near
the center of the bed and consequently there may
be a low validity for HEST to simulate airblast-
induced ground motions.
/. BLEST (Berm Loaded Explosive Simulation
Technique) is a technique to supplement the HEST
method by using an array of shallow-buried
charges in the area adjacent to HEST structure,
initiated in proper sequence with the HEST Event,
it generates an extended downward loaded area,
minimizing, for a while, the undesired outward and
upward motion in the vicinty of the HEST area
itself. The design permits simulation detonations
that allow the test structure to react fully to the
primary stimulus before boundary effects distort
the loading. A relatively new addition to the sim-
ulation techniques, it holds promise of reducing the
size of the HEST structure itself while improving
simulation. For further information on the theory
and on test results, see Schrader et al. (1976) and
test reports on the HARDPAN I test series that
used the method.
B-15
TM 5-858-6
Table B-ll. Chronology of High-Explosive Tests
TABLE B-ll. CHRONOLOGY OF HIGH-EXPLOSIVE TESTS
DATE
TEST
LOCATION
SIZE OF CHARGE; PURPOSE OF TEST
Feb 1964
Flat Top II
Nevada
20t TNT, spherical, half buried, desert playa, dry. To develop
theoretical methods for predicting ground motion and cratering.
Mar 1964
Flat Top III
Nevada
ZOtTNT, spherical, half buried, desert playa, wet.
June 1964
Flat Top I
Nevada
20t TNT, spherical, half buried, limestone, dry.
July 1964
Snow Ball
Canada
SOOt TNT, spherical, surface. To simulate a Ikt surface nuclear
burst.
1966-1967
Distant Plain:
1966-1967
Event 1
Canada
20t TNT, spherical, on 85 ft tower.
1966-1967
Event 2a
Canada
Gas filled balloon, hemisphere on surface. Equivalent to 20t TNT.
1966-1967
Event 3
Canada
20t TNT, spherical, surface. To study close-in ground shock
phenomena.
1966-1967
Event 4
Canada
50t TNT, Hemisphere, surface. To study blow-down effect in a
forest.
1966-1967
Event 5
Canada
20t TNT, spherical, surface, frozen ground. To study cratering
and ground shock in frozen ground.
1966-1967
Event 6
Canada
lOOt TNT, spherical, surface. To study scaling factors by com-
paring results for Events 6 and la, using identical instrument
patterns.
1966-1967
Event la
Canada
20t TNT, spherical, center 29.5 ft above ground. To compare
scaling factors with Event 6 above.
Aug 1968
Prairie Flat
Canada
SOOt TNT, spherical, surface. To further study scaling factors
by comparison with Distant Plain Events 6 and la.
Oct 1968
Mine Under
Utah
lOOt TNT, spherical, 2 x charge radius above surface. To study
cratering and shock effects over rock surface.
Nov 1968
Mine Ore
Utah
lOOt TNT, spherical, 0.9 x charge radius below surface. To study
cratering and shock effects over rock surface.
Sept 1969
Mineral Lode
Utah
14t slurry, sealed cavity, 100 ft below surface. To study ground
motion with fully contained detonation in rock.
Oct 1969
Mineral Rock
Utah
lOOt TNT, spherical, surface. Further study of ejecta and motions
in rock surface.
Aug 1970
Dial Pack
Canada
SOOt TNT, spherical, surface. Further study of scaling factors,
for comparison with Distant Plain. Events 6 and la, and Prairie
Flat, using same configuration over same geologic medium.
July 1972
Mixed
Colorado
SOOt TNT, spherical, surface. To simulate a 1.8 kt surface nuclear
Sept 1971
Middle
Gust I
Colorado
20t TNT, spherical, half buried, clay over shale with water table
10 ft below surface. Middle Gust series to study effect of water
near surface.
Dec 1971
Middle
Gust 11
Colorado
lOOt TNT, spherical, 2 x charge radius above surface, clay over
shale with water table 10 ft below surface.
Apr 1972
Middle Gust
Gust III
Colorado
lOOt TNT, spherical, surface, wet, clay over shale with water
table 10 ft below surface.
June 1972
Middle Gust
Gust IV
Colorado
lOOt TNT, spherical, surface, clay over shale with no near-surface
water.
Aug 1972
Middle Gust
Gust V
Colorado
20t TNT, spherical, half buried, clay over shale with no near-
surface water.
Spring 1976
Pre-Dice Throw
I 4 II
New Mexico
120t ANFO (lOOt TNT equivalent) Cylinder plus hemisphere, surface;
desert alluvium ground-s*hock measurement and exposure of structures
and equipment.
Oct. 1976
Dice Throw
New Mexico
600t ANFO (SOOt TNT equivalent) Cylinder plus hemisphere, surface;
desert alluvium air-blast exposure of equipment and structures.
1
U.S. Army Corps of Engineers
B-16
TM 5-858-6
B-3. Direct-induced high-explosive
simulation technique (DIHEST).
a. The DIHEST development began in 1967 and
uses a buried array of high explosives to produce a
specified particle velocity history in the soil at a
given range from the array. Because of time con-
straints, the developmental DIHEST study was re-
stricted largely to simultaneous detonation of rec-
tangular, planar, and vertical explosive arrays
(table B-4).
b. In a buried retangular array of N sperical
charges, one can argue that the peak horizontal
particle velocity from the array can never be
smaller than that obtained from one of the N
sources (for sufficiently close source spacing). Fur-
thermore, this lower bound should be approached
as one moves closer and closer to the array. On the
other hand, the peak particle velocity away from
the explosive array should be a function only of the
array geometry and total yield, and should be in-
dependent of the number of sources involved. In
fact, it is expected that a reasonable upper bound
(approached asymptotically with increasing range)
is given by the peak particle velocity from a single
spherical source of the total array yield.
c. A summary of particle velocity histories mea-
sured in the vertical symmetry plane at ranges of
30 and 60 ft from the DIHEST array suggests that:
Horizontal particle velocity signatures were
reasonably consistent within the lower
two-thirds of the DIHEST depth.
Horizontal particle velocity signatures were
essentially the same form to be expected
from contained spherical charges (in
particular, no appreciable shear effects
were observed).
Horizontal peak displacements were consis-
tent with those expected from a tamped,
burried, spherical explosive of the same
yield as the DIHEST array.
Significant upward late-time motions asso-
ciated with free surface effects would be
produced by the DIHEST.
d. The DIHEST technique simulates, in a variety
of geological formations, direct-induced ground mo-
tions expected from a nuclear device effecting
buried strategic systems or a part of such systems.
DIHEST coupled with HEST provides a capability
of producing airblast as well as direct-induced
ground motions on a variety of test items. Such
testing is very expensive ( $2 XlO 6 ), but may be a
good value as the only viable technique under the
ban on atmospheric nuclear testing. A chronology
of DIHEST testing is included in table B-10.
B-4. High-explosive surface burst.
a. When nuclear experiments in the atmosphere
were suspended in May 1963 by a presidential or-
der preceding the nuclear test ban treaty, it was a
crucial time for the suspension because a series of
nuclear and high-explosive experiments were under
way to compare ground motions from a nuclear
surface burst with ground motions from a high-
explosive surface burst.
6. Flat Top was a series of 20-ton HE experi-
ments using blocks of TNT with the center of the
spherical mass at the ground surface. Two experi-
ments were conducted at an alluvium site and the
third at a limestone rock site. In alluvium, the
peak radial displacement measured near the sur-
face was 24 in. at the 500 psi overpressure station.
In limestone, the displacements were somewhat
less (data were not reliable for the experiment in
limestone).
c. Over the past decade, many HE field tests
using built-up charges of high explosives have been
conducted to satisfy the needs of specific programs.
These tests often have been conducted in remote
areas over land and water and in an arctic environ-
ment. Measurements included transient overpres-
sure, ground shock and ground motion, water shock
and water waves, as well as crater size and ejecta
distribution.
d. Charge sizes up to 500 tons of TNT have been
used. There are certain limitations involved with
even these large-sized HE tests. For example, if the
charge is detonated on or close to a soil surface,
the crater formed interferes with the placement of
buried or surface targets.
e. Two installations having permanent facilities
to conduct large HE tests, 100 to 500 ton, are the
Nevada Test Site (NTS) located near Las Vegas,
Nevada, and operated by the U.S. Atomic Energy
Commission; and the Defence Research Establish-
ment, Suffield (ORES) located near Medicine e
Hat, Alberta, Canada, and operated by the Defence
Research Board of Canada. Large HE tests con-
ducted at remote sites other than NTS and Suffield
are expensive, and every effort is made to include
in each test as many of the requirements as possi-
ble of the various defense and armed forces agen-
cies.
/. HE tests to investigate various effects of air-
blast and ground shock are tabulated in table B-12.
The tabulation begins with the Flat Top series and
B-17
TM 5-858-6
TABLE B-12. GRABS TESTS; GIANT REUSABLE AIRBLAST SIMULATOR
DATE
July 1971
through
1973
TEST
D-l
D-2
PI-1
PI-3
PI-4
PII-1
PII-2
PII-3
TEST DESCRIPTION
GRABS tests have been conducted at Kirtland AFB, using a buried concrete
cylinder 18 ft dia. x 30 ft deep, flush with the surface. Test objectives
were to study structure/media interaction using a stiff structure of
simple geometry within which well-defined soil media could be provided.
The GRABS facility is a blast pressure chamber using a HEST-type
environment.
Development test: to test the facility and obtain soils data.
Development test: to test the facility and obtain soils data.
Two models, stacked one on top of the other, in a dry sand medium.
Single model, 15 ft high, in dry sand medium.
Same model as PI-3, in wet sand medium
20-ft articulated structure, resting on floor of dry sand medium.
20-ft articulated structure, flush with surface, wet sand medium.
Upper half of PII-2 structure, resting on floor, dry sand medium.
U.S. Army Corps of Engineers
NOTE: This series of tests is expected to continue.
goes through the Middle Gust series.
B-5. Underground nuclear tamped
burst.
a. Since the test ban treaty, two important un-
derground nuclear experiments have been
performed. HARDHAT and PILEDRIVER. These
experiments were performed in the granite rock in
Nevada, at depths of about 1500 ft. A series of
tunnel liners were located at varying ranges from
ground zero (GZ), all in the high stress region, 0.5
kb to 4 kb. (Various liner concepts were used, such
as liners with backpacking and rockbolting, and
concrete liners poured directly against the rock.) A
great deal has been learned about the cavity liner
design for direct-induced motions.
b. The experiments have also demonstrated the
capability to produce large ground motions
expected from megaton surface bursts. From ex-
periment to experiment, however, the data scatter
when scaled can differ by an order of magnitude;
testing a prototype facility for defined criteria
could be very difficult. This data scatter in test
results may show the uncertainties in present-day
design criteria.
c. Tamped nuclear experiments have been recom-
mend for testing Air Fence Launch Control Facility
and Launch Facility structures, and may produce
the best simulation of direct-induced motions.
Since calculations substantiate test results for peak
stress, it is reasonable to expect that tests can be
designed to produce specified peak stress levels at
specified structure locations. The uncertainty in ex-
pected ground motion (primarily displacement)
must be considered in the design of the test.
B-6. Underground nuclear tunnel
experiments.
B-18
TM 5-858-6
a. Underground tests of nuclear weapon effects
require the construction of a tunnel complex for
installation of the weapon and the test specimens
and apparatus, combining several experiments to
get maximum use of the site. For moderate in-
cremental program cost, structural testing experi-
ments are added to events primarily designed for
other experiments. The MIGHTY EPIC/DIABLO
HAWK pair of events is such an instance.
6. The MIGHTY EPIC event at NTS was de-
signed primarily to evalulate the radiation physics
of a nuclear device using a line-of-sight (LOS) pipe.
An LOS pipe is a conical tube aligned with its
projected apex at the center of the nuclear device
and extending radially outward for as much as a
thousand feed or more. An LOS pipe is an expen-
sive device to fabricate; in addition to requiring
safety closures and test stations in various loca-
tions, it must also be capable of sustaining a hard
vacuum on the inside (required to prevent attenu-
ation of radiation along the interior of the pipe).
MIGHTY EPIC is a landmark event to designers of
hardened structures because of other programs
that were conducted at the same time.
c. For the structures program, several types of
cylindrical and spherical structures were tested.
Three separate drifts were constructed at ground
ranges from the nuclear device that would produce
the design stress level, one-half design level, and
twice design level. One of the novel features of this
experiment was the placement of nine copies-as
identical as could be constructed of a spherical
reinforced concrete structure. They were installed
in sets of three at each stress level. It was expected
that the close-in models would fail, the mid-range
models would sustain moderate damage, and the
distant units would be unscathed. In general, the
actual test results followed theory, and the replica-
tion of test structures at each stress range gave a
data base for evaluating the random variations of
design parameters. Additional benefits will accrue
from the DIABLO HAWK event (see e below).
d. Another objective of the MIGHTY EPIC event
was to test theory that structures sited in a hard
medium overlaid by an extensive layer of more
porous medium would experience a more moderate
environment than if they were sited at an equal
depth in an all-hard medium. MIGHTY EPIC was
sited in a quartzite bed overlaid with tuff. A useful
amount of data was collected with which it is
possible to evaluate the concept. The serious re-
searcher is encouraged to seek out the data in the
classified MIGHTY EPIC progress reports.
e. DIABLO HAWK, a follow-on to MIGHTY
EPIC planned for the same test bed, is designed
and will be located to provide a repeat loading of
the structure tested in the MIGHTY EPIC event.
This second loading of the structures will provide a
stress wave propagating approximately 90 deg to
the original MIGHTY EPIC stress wave direction.
Such cyclic loading is rare in dynamic testing, out-
side of small-scale models in laboratories. Access to
the structures was gained by retunneling into the
test bed and opening the access ports. Extensive
photographic coverage and dimensional mapping
were performed after the MIGHTY EPIC event and
have become "pretest measurements" for the DIA-
BLO HAWK event, scheduled for some time in
1978.
B-7. Giant reusable airbiast simulator
(GRABS).
a. The GRABS is a cylindrical silo, 18-ft dia. by
48-ft deep and lined with reinforced concrete, con-
structed in a massive limestone formation at Kirt-
land AFB. New Mexico. It was developed to provide
a two-dimensional zxisymmetric test facility for
evaluating the computational predictions of the
vertical motions of missile silos from overpressure.
6. A preselected amount of soil (up to 30 ft) is
placed in the lower portion of the facility along
with instrumentation and model structures, and a
modified HEST is used to generate overpressure
within the facility. This technique has the dem-
onstrated ability to reproduce reasonably the air
pressure history up to the -1800 psi overpressure
level from a 1-Mt surface burst. For a predeter-
mined time, the technique confines within the fa-
cility a high-explosive detonation in a finite vol-
ume. This is done by using soil as a surcharge
above an explosive cavity. The peak pressure, ini-
tial decay, and late-time decay can be controlled by
variations in explosive charge density, initial explo-
sive cavity volume, and the height and density of
the surcharge material, respectively. The detona-
tion projects the surcharge into the air, thereby
eliminating the need for reaction devices. The sur-
charge support system is designed so that no
braces extend to the test-bed; thus only the detona-
tion shock is transmitted to the test-bed. Table
B-12 is a list of tests conducted in the GRABS
facility.
B-8. BMP simulation methods.
a. The EMP associated with a nuclear explosion
can be considered an insidious effect, for it can do
damage to unprotected systems at distances from
the blast where other effects are not bothersome
B-19
TM 5-858-6
(high-altitude bursts, for instance). However, its
effects can be guarded against, and its consider-
ation should be carried throughout the design and
construction phase to achieve the best results for
the least cost. Retrofitting EMP protective devices
to a finished facility can be very expensive. Testing
for design and hardness verification should be done
at each significant step of the way. A summary of
available facilities and techniques follows.
b. In the last decade, a large amount of research
has gone into EMP and its cause, effects, and miti-
gation. Three documents of major significance to
designers of hardened facilities summarize the
state of the art quite well: GE-TEMPO, 1974 a;
Schlegel, 1972; Bridge-Emberson, 1974. The follow-
ing sections are extracted from the DNA EMP
Handbook because it sets forth cogently the idea
that attitude and prior analysis are so vital to the
conduct of meaningful tests; less dedicated testing
becomes mere busy work.
c. In general, EMP testing is expensive, time
consuming, and filled with pitfalls that make it
difficult to obtain credible results. Factors involved
in deciding whether to engage in a test program
and how to set it up include:
Priority of assessing vulnerability of the sys-
tem under consideration
Simulation requirements based on system defi-
nition and postulated threat
Costs involved
Real-time requirements
Once the decision to test has been made, its success
or failure depends, to a great degree, on the exper-
ience and attitude of the individuals directing it. A
good test is one that:
Is viewed with a hypothesis at hand, derived
by analysis;
Includes within its concept of accomplishment
a statistical view of the problem;
Is conducted by experimenters who are con-
stantly prepared to reject their hypothesis
during the test, based on the evidence at
hand, and who are willing to develop and
investigate a new hypothesis if required.
d. A test should constantly be monitored by
qualified analysts. For large-scale tests the an-
alysts should be on-site as well as off -site to assess
the progress of the test as it proceeds, redirect it if
necessary, and see that the results are credible.
The importance of analysis before the test cannot
be overstressed, because it forms the necessary ba-
sis for continuous evaluation in terms of success or
failure as the experiment proceeds. The required
depth and extent of this analysis are matters of
judgment, but even rough approximations are use-
ful. Analysis is extremely difficult if it attempts to
achieve high accuracy; even a transferfunction pre-
diction for a real system can prove to be a chal-
lenging exercise. However, gross estimates must be
made to determine feasibility in reasonble time and
cost; these are based on generic groupings of the
system and parametric analysis of these groupings.
In this type of analysis, there is no substitute for
experience; the experienced analyst has at his fin-
gertips a storehouse of analytical tools, experimen-
tal data, and knowledge of what has and has not
succeeded in the past. This perspective is a vital
factor in achieving reasonably analytical results in
a short time.
e. In EMP tests, nothing is precise. Neither the
simulation, nor the instrumentation, nor the data
reduction, nor the system behavior itself is ab-
solute. All vary, and many introduce errors. It is
essential that this be recognized early in the pro-
gram. The fact that precision is impossible should
not be interpreted as an excuse for carelessness. To
the contrary, every reasonable effort should be
made to minimize errors everywhere so that at the
end of the program an assessment can be made
that is as free from uncertainty as possible.
/. The problem must also be viewed statistically,
because the system under test may vary from unit
to unit. Early recognition of this system variation
will permit a more orderly pursuit of the end goal.
If errors and system variability are not bounded,
the assessment of vulnerability can be totally in
error. If errors and uncertainties are not mini-
mized, the system may be penalized by excessive
hardening requirements to cover not only the EMP
effect but the large errors and uncertainties asso-
ciated with the assessment of that effect.
g. It is important to think carefully at the begin-
ning of test planning about what is desired as an
output of the test and exactly how that result will
be used in the assessment. Voltage and current
waveforms might be collected (time domain) at low
level with the idea of using linear extrapolations in
time domain are invalid if the system is nonlinear.
To cover this uncertainty, a high-level simulation
using a reasonable pulse waveform is mandatory.
At the same time, an analytical model of the sys-
tem is highly desirable. Alternatively, transfer
functions from external fields to voltages (for cur-
rents) in critical locations might be obtained
(frequency-domain) with the idea of using these in
analytical predictions. However, accurate transfer
function determnation may require a simulation
experiment different from that used in voltage or
current determinations, and again the validity of a
B-20
TM 5-858-6
transfer function depends on system linearity.
Thus, obtaining both representative timedomain re-
sponses and system transfer functions with one
simulation may not be compatible goals, and it is
important to know what is needed and to have an
alternative if the system proves to be nonlinear.
h. If the system behavior is truly nonlinear at
the higher levels, then probably the only way to
predict this behavior is by developing an analytical
system model, including models of the characteris-
tics of the important nonlinear devices or system
segments. From this model, valid time-domain pre-
dictions can be made on a computer.
i. In general, the problem of assessing a system's
vulnerability to EMP is not unlike a massive
trouble-shooting problem in which the system may
have several faults that must be located and cor-
rected. The process is inherently an iterative one in
which the experimenter learns, little by little, what
the causes and effects are in the system and how
detrimental effects can be prevented. Results to-
ward this end will be achieved sooner if the data
are collected carefully right from the beginning,
since poor data can lead to erroneous conclusions,
confusion, and delays.
j. The two approaches that can be used in at-
tempting to establish criteria for what should be
measured are to:
Work directly on circuits believed to be most
critical and measure the input voltages of
these circuits (a hazardous approach)
Work into the system from the outside, measur-
ing first what the EMP induces on the
exterior of the system, then systematically
tracing the current flow from there to cab-
ies, and along these cables to subsystem
black boxes
k. The direct circuit approach is plagued by
many traps. Voltage at the input of a particular
circuit ignores the fact that the EMP may be com-
ing in on a different circuit-interface wire such as
ground or power or some other lead. To evaluate
the "input" of EMP to that circuit, it would be
necessary to measure the current or voltage on
every wire leading to it. This may so load down the
circuit (probes have capacitances that may not be
negligible in their effects at these frequencies) that
the data are useless. Connecting several probes into
a circuit without bringing in some EMP currents is
also a difficult matter. One of the greatest
weaknesses of this approach, however, is that it
may provide the semblance of data assessment
without any real understanding of why the signal
is at the circuit, why it looks as it does, and how it
can best be eliminated. This type of premature
assessment of systems is hazardous.
I. When a system is worked into from the out-
side, an overall understanding of system behavior
is obtained sooner. At the same time, enough data
can be obtained at subsystem or black-box inter-
faces to permit more detailed investigations to be-
gin in the laboratory. Though there are some ex-
ceptions, this procedure is usually best.
m. What should be instrumented are those
things that will answer these key points:
How much current is induced on the exterior
of the system.
How much of this external current gets inside
the system.
How this energy gets inside.
Where this energy goes and how it is distrib-
uted.
What this energy does to each subsystem.
How any detrimental effects can be elimi-
nated.
n. These questions should guide the selection of
points to be measured. Having selected all of the
desired measurement points, it is probable that
there will be too many to instrument at one time
because of internal space limitations or other con-
siderations. In this case, the measurements are
best performed a few at a time, because instrumen-
tation does load the system and change current
amplitudes and distributions to a certain extent,
and thus should be kept to a minimum.
o. Electromagnetic scale modeling is an impor-
tant alternative to full-scale testing under the fol-
lowing conditions:
Test facilities or available equipment are at a
premium.
The system to be tested is very large.
The system dedication cost for full-scale test-
ing is high. In
addition to the advantages of modeling under these
conditions, benefits can be derived as follows:
Sensors can perhaps be better placed during
full-scale testing as a result of model ex-
periments.
Design modifications or cable reroutes can be
made prior to fullscale testing.
Electromagnetic angles-of -arrival can be deter-
mined for worst- and best-case conditions.
Effects of change in the conductivity of sur-
rounding media can be explored to an ex-
tent not possible in full scale.
Estimates can be made of some of the re-
sponses of a complex system prior to full-
B-21
TM 5-858-6
scale testing.
Quantitative data can be obtained to validate
analysis.
p. It should be pointed out that because of the
difficulty in introducing minute openings or poor
bonds into models, and since these often control
inferior fields, the usefulness of modeling is or-
dinarily limited to the measurement of limited
value, and are generally appropriate only in con-
firming previous analysis. However, once the ex-
terior fields, voltages, and currents are known for a
complex structure, perhaps having cable runs, ana-
lysis can often yield internal field quantities of
interest.
q. In actually setting up a scale model test, the
following should be kept in mind.
(1) Broadband pulse response determination in-
volves much more than does a steady-state, single-
frequency response test.
(2) Special electromagnetic illumination sour-
ces are required that are coherent, have uniform
time delay, and use antennas with constant effectiv
height.
(3) Special modeling techniques are required
for studying exposed conductors passing over or
within a lossy dielectric, such as earth. A pulse-
type waveform can theoretically be replaced by a
continuous wave (CW) source with a sensing sys-
tem that references the sensed CW signal to a
reference phase from the source. Complex Fourier
transfer functions can be developed by computer
processing the recorded data. However, long sweep
times are required to ensure that all narrow band
responses are adequately explored, and the actual
physical implementation of such an approach in
the microwave band poses additional difficulties.
On the other hand, the use of scaled real-time
waveforms allows quick development of actual re-
sponses, from which complex Fourier transfer func-
tions can also be developed with the aid of comput-
ers.
r. Scaling relationships are derived from the the-
ory of electrodynamic similitude. We define the
modeling factor, M, by:
M =
D s
where
D a = A dimension of the actual system to be
modeled
D s =The same dimension of the scaled system
For example, when a 300-ft long structure is scaled
down to a 30-ft long model, this 1/10 scale model
has a modeling factor M 10.
s. The relations between scaled and actual quan-
tities are:
Model Size D s = d a /M (B-2)
Frequency w s = Mo> a (B-3)
Conductivity <T S = Mcr a (B-4)
Dielectric Constant e s = e a (B-5)
Permeability y" s = j^ a (B-6)
t. A plane wave propagating in the positive z
direction in an imperfect dielectric can be char-
acterized by H(z,t) =H m e- zej(wt ~ z) (B-7)
where H m is the wave amplitude at z 0, a describes
the wave attenuation in the dielectric, and B is the
phase constant, a and B are real and given by:
-l
1/2
(B-8)
(B-9)
The wavelength, A. , in the dielectric is given by
X=27r//3
(B-10)
and from equations B-8 through B-10, it is seen that
, /3 , and X scale as follows:
(B-ll)
(B-12)
(B-18)
X s =X a /M
u. A summary of EMP simulation test facilities
is shown in table B-9. The listing is not all-
inclusive by any means but does give an indication
of the types of fixed facilities (relative) that are
available. In the extensive literature available,
methods are discussed for establishing test arrays
at the facility to te tested.
v. Note that in the tables the simulator type
includes stationary or fixed simulators, and porta-
ble ones. The only simulator listed that can be
moved about and is not fixed is RES-I, which is
helicopter-transportable. Pulse variability figures
represent uncertainties in amplitude and decay
times, and jitter represents the uncertainty in the
firing time. Cycle time is the time between pulses.
B-22
TM 5-858-6
B-9. Blast simulation techniques for
testing air-eotroiiiment systems and
blast closures.
a. Comments are limited to methods available
for testing overpressure on the performance of har-
dened air entrainment systems and blast closures
under conditions simulating a nuclear attack. Tests
specifically intended for the assessment of debris
effects do not presently exist; therefore, comments
in this area are directed to desirable tests and
possible test techniques.
6. Shock-tube, implosion driver, and underground
field tests have been instrumented to test overpres-
sure effects on blast valves and air-entrainment
systems (tables B-l through B-4). The blast simula-
tor at the WES is capable of producing environ-
ments with an upper pressure limit of 1000 psi; the
physical size of the test chamber requires subscale
models. The current pressure rise time is much too
low for meaningful air-entrainment system tests,
and it is not considered a useful facility for testing
present or future air-entrainment systems.
c. Surface debris entering air-entrainment sys-
tems during a nuclear attack will come from four
sources:
Particulate material entrained in the air
shock flow
Surface material from cratering moved past
the entrance
Crater ejecta descending from aerial trajec-
tories
Particulate fallout from the nuclear cloud
d. Surface debris from overpressure flow will be
relatively small particles carried into the air en-
trainment systems by the flow velocity behind the
air shock. This material will be distributed
throughout the air entrainment system, although
very little material should reach the vicinity of the
blast valve. Test simulation of this debris will be
very difficult because a method of entraining the
proper particle size and velocity distributions is not
available. Some of this debris will be removed from
the facility during the negative overpressure phase,
and it is not expected that the residue will con-
stitute a threat to the facility. Future improve-
ments in the analysis of two-phase shock flows
may lead to tests that might accurately assess the
distribution of this material in air entrainment
systems (table B-10).
e. Cratering causes most of the debris impinging
on facilities. For sufficiently large weapons and
close detonations, the air-entrainment system sur-
face entrance may be engulfed in debris material
from cratering. A substantial amount of this debris
may collect in the debris pit of the air entrainment
systems, but very little should enter the blast-valve
trigger or delay lines.
/ Simulation of this debris flow is complicated
by lack of test data from nuclear blasts, and lack
of adequate scaling principles from HE to nuclear
blast. Tests of some value could be performed by
using large chemical explosives in close proximity
to full or scale models of air-entrainment systems.
Similarity of test site media to that of proposed
facility locations would be important, since scaling
of explosive effects between various types of soils is
not well understood. Tests of this type would be of
use in determining the likely distribution of var-
ious sizes of debris particles, the nature of bloc-
kages of the surface entrances, and methods of
eliminating such blockages. To reduce the expense
of these tests, combine them with other large HE
programs, such as those conducted at DRES, Al-
berta.
g. Debris from the nuclear cloud will settle into
the facility for some time after an attack, but will
be concentrated primarily in the debris pit. Fallout
distribution was studied in some detail at the time
of surface nuclear tests, and can now be predicted
with some assurance. A test that might be ap-
plicable for assessing the distribution of fallout
material in an air-entrainment system could be
performed by allowing equivalent size particles to
settle into the entrance while the ventilation sys-
tem was operating at a level appropriate to postat-
tack conditions.
h. The distribution and importance of initial at-
tack debris could be significantly altered by subse-
quent blasts. If multiple attacks are part of the
design threat, place debris equivalent to that from
an initial attack in an air entrainment system
prior to performing a blast simulation
B-23
c
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TM 5-858-6
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C-2
TM 5-858-6
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C-4
GLOSSARY
Acceptance
Region:
Air-Entrainment
System:
Bias Errors:
Binomial
Distribution:
Blast Attenuator:
Blast Valve:
Burst Conditions:
Chi Square (X 2 )
Goodness-of-Fit
Test:
Confidence
Coefficient:
The range of a statistic (in this
text, the t-statist ic) for which
the hypothesis is accepted as
true.
Accomplishes a continous or pe-
riodic transfer of air (gas) be-
tween the atmosphere and the
facility.
Systematic errors resulting
from imcomplete or inaccurate
modeling, measurement errors,
etc.
A distribution where the values
r/n for r 0, 1, ..., N have the
frequencies
n!
r!(n-r)!
P r (l-p) n - r
where p is the probabilty occur-
rence.
A device for reducing in an air
entrainment or exhaust duct.
Wall friction, flow restriction,
and expansion chambers are of-
ten used
A valve that prevents entry of
overpressure into hardened fa-
cilities.
A description of the location of
point of burst relative to the
ground surface and to the tar-
get.
A means of measuring the dis-
crepancy between the Probabil-
ity Density Function (PDF) ex-
hibited by a data set and that
for Gaussian, i.e., normal, or
other hypothetical distribution.
The confidence level associated
with the confidence interval.
Confidence
Interval:
Continuous
Wave:
Correlation
Coefficient:
Delay Line:
Deterministic:
DIHEST:
The range within which an es-
timate will fall for a specified
level of confidence, e.g., 90% of
the time the difference between
the mean of a normal popula-
tion and the mean of an n-
number sample will fall
between 1.96oY\/n.
A steady state excitation signal,
e.g., cos cot, as opposed to a
transient or impulsive
excitation. Frequency sweep or
frequency stepping may be used
to cover the broad frequency
range of interest.
The ratio of the covariance of
two random variables to the
square root of the product of
their variances, i.e.,
That portion of an air-
entrainment system between a
sensor and blast valve that al-
lows valve closure before over-
pressure arrival.
having an assigned value; with-
out uncertainty.
Direct-Induced High-Explosive
Simulation Technique. A
method using a buried array of
high-explosives to producje a
specified particle velocity time-
history in the soil a given dis-
tance from the array. Coupled
with HEST it can produce air
blast and direct-induced ground
motions on various targets.
Glossary- 1
TM 5-858-6
Direct Injection:
ORES:
EMP:
Expansion
Chamber:
Failure Modes:
Failure-Oriented
Analysis:
Excitation of a system or sys-
tem element by direct applica-
tion of electromagnetic signal,
force, or displacement rather
than by the application of such
loads that pass through and are
modified by intermediate
elements such as protective
structures and shock-isolation
system or shielding.
Defense Research
Establishment, Suffield. A
semi-remote research facility
near Medicine Hat, Alberta,
Canada, where experiments re-
quiring extensive land area can
be conducted. Site of previous
100 ton and 500 ton high explo-
sive tests.
Electromagnetic Pulse.
Associated primarily with the
high intensity radiation and
conduction fields induced by nu-
clear explosions. Can produce
extremely high currents in con-
ducting element, disrupting or
distroying electronic
components.
A type of blast attenuator for
air entrainment/ exhaust
systems which relies on the
pressure-averaging effect of
chamber fill time to mask or
attenuate the maximum over-
pressure associated with sharp
peaks
Identifiable mechanisms of sys-
tem or system element failureks
e. g., communication system
failure modes may include blast
damage to antenna, EMP Bur-
nout of antenna lead, ground-
shock damage to antenna lead,
EMP burnout of transmitter,
shock and vibration damage to
transmitter, power outage, etc.
An analysis that examines
occurrence/ nonoccurrence of
failures capable of preventing
mission function.
Fault Trees: A graphical presentation of the
relationship between loads and
failure modes and of their rela-
tion to system composition from
the element through overall
system levels.
Functional Block
Diagram:
GRABS:
A pictorial presentation of the
operating relationship between
system elements.
Giant Reusable Air-Blast Sim-
ulator. A large Cylindrical silo
in massive limestone at Kirt-
land Air Force Base, New
Mexico. Designed to provide a
2-dimensional axisymmetrical
test bed for air blast overpres-
sure stimulus.
HARDHAT: A code name for an
underground tamped nuclear
event to evaluate hardened
structural designs.
Hardness Satisfaction of hardness
Compliance: requirement.
Hardness The process of determining that
Verification: a system or system element has
at least the resistance
(hardness) claimed for it.
HEST: High-Explosive Simulation
Technique. A method for simu-
lating nuclear air-blast-induced
ground motion.
Hydraulic Surge: Water hammer.
Ignorance
Factor:
impendence:
A measure of that portion of
the uncertainty resulting from
incomplete knowledge of the
phenomena or from bias or sys-
tematic error in measuring the
phenomena, the uncertainty not
related to the truly random
natur of the phenomena.
Mechanical impendance, the ra-
tio of the acceleration of a me-
chanical system to the
sinusoidal force exciting it:
Glossary-2
TM 5-858-6
Intake Structure:
Level of
Significance:
That portion of an air-
entrainment system where air
enters the system.
a, the chance of rejecting a true
hypothesis; the complement of
the level of confidence.
Network Logic
Diagrams:
A graphical means of present-
ing the functional relationships
of system elements, loads, and
failure modes; similar to flow
diagrams used in computer pro-
gramming.
Lognorma!
Distribution:
Low-Level
Transient:
A statistical distribution in
which the logarithm x of the
variable y is normally distrib-
uted; its probability density
functions:
Nonparametric:
: exp
where oy ny is the standard de-
viation of n y and my is the
median value of y.
Excitation by a transient signal
simulating the threat time his-
tory but at amplitudes below
those specified for the threat
level.
Normal
Distribution:
Used here to denote those situ-
ations where either (1) the dis-
tribution is not a member of a
known class (normal, lognormal,
binomial, etc.) or (2) there are
not enough data to allow iden-
tification of the distribution.
Under these conditions
estimates of parameters such as
the mean and variance cannot
be obtained. However,
confidence intervals for quantit-
ies can be obtained.
Distributed in a Gaussian man-
ner; i.e., having the probability
density function
exp -(x-/z) 2 /(2o- 2 )
Minimum Sample
Size:
Mission Critical
Functions:
Monte Carlo
Method:
I
Mounts and
Fasteners:
The smallest sample from
which a valid statistical infer-
ence can be made.
Those functions that are neces-
sary to the execution of a sys-
tem primary mission.
A technique that obtains pro-
babilistic approximations to
problems by executing a large
number of simulation problems
with parameters defined by sta-
tistical sampling.
The mechanical components
used to connect equipment to
protective structures, platforms,
racks, shock-isolation systems,
etc.
where u =mean and o- 2 =va-
NTS:
One-Sided
Procedure:
Overburden:
Penetration:
PILEDRIVER:
rance.
Nevada Test Site,
control of DOE.
under the
A statistical test wherin the hy-
pothesis will be accepted if the
statistic satisfies a one-sided
condition of the form t x.
Overlying soil or rock. .
An opening that pierces the
protective shell of a hardened .
facility, such a a conduit for
communication or power cables.
Code name for an underground
tamped nuclear event to evalu-
ate concepts of hardened struc-
ture design.
Glossary~3
TM 5*858-6
Population:
Probabilistic
Assessment:
Probability
Density Function:
Probability
Distribution:
Probability of
Success:
Protective
Facilities:
Pulse-Train
Simulation Test:
Radiation
Shielding:
The set of objects or measur-
able effects having some com-
mon observable properties; for
example, all Minuteman Launch
facilities, or all thermo-nuclear
explosions.
methodology for addressing the
influence of uncertainties in
loads and resistances when as-
sessing the hardness and
survivability /vulnerability of
hardened facilities.
A mathematical statement of
the frequency of occurrence of
possible values of a random
variable (see, for example, Nor-
mal Distribution).
A function that assigns to each
possible value of a random vari-
able the probability of its occur-
rence. For continuous rando
variables, the integral of the
probability density function,
also known as the cummulative
distribution function.
In this text, probability that a
resistance exceeds its
corresponding load, i.e., the
probability that failure will not
occur.
Facilities whose function is to
protect material, equipment,
personnel, and mission capabil-
ity from the harmful effects of
nuclear weapons.
A test in which system response
is excited by a train of pulses
designed to simulate the threat
driving forces.
Material that prevents penetra-
tion or reradiation of nuclear
radiation environments a, (3 ,
and Y-radiations from nuclear
weapons.
Random Errors:
Random
Uncertainties:
Repetitive Pulse:
Resistance:
Resistance
Design Goal:
Shock-Isolation
System:
Stationary Field:
Survivability:
Survival
Probability:
System:
System
Engineering:
Errors distributed according to
chance, as opposed to bias or
systematic errors.
Uncertainties in the value of an
attribute resulting from its ran-
dom nature.
Excitation by a pulse train
which covers the frequency
range of the threat environment
but may not simulate the time
history of the threat pulse.
Ability to withstand nuclear
weapon-effect loads.
The level of resistance to be
achieved to satisfy survivability
requirements. Often stated in
terms of local free-field nuclear
weapon-effect environment am-
plitudes.
A system mechanical, hydrau-
lic, pneumatic, or hybridthat
attenuates the shock and vibra-
tion environment transmitted
throug its elements.
An EMP simulation for small
components not sensitive to the
transient nature of threat EMP
pulses.
The probability that a
facility/Subsystem/component
failure-mode will functionally
survive a nuclear-weapon attack
and retain its physical integrity
during the specified endurance
period.
The probability that system or
system element resistances ex-
ceed their corresponding loads.
A combination of elements, sub-
systems, or pieces of equipment
integrated to perform a specific
function.
A science dealing with the de-
sign and performance of inter-
connected components, sub-
systems, and systems.
Glossary-4
TM 5-858-6
I
System Hardness
Level:
Systematic Error:
Systematic
Uncertainties:
Tap:
Thermal
Shielding:
TTCP:
Threat Scenario:
Transfer
Function:
The maximum load level for
which a system retains
functional capability at a pre-
scribed level of confidence.
An error resulting from bias in
measurement, and not from
chance. In this text, ignorance
or imcompleteness of knowledge
is treated as a systematic
(nonrandom) error.
Uncertainties due to unknown
systematic errors or ignorance
(incomplete knowledge).
1 tap = 1 dyne-sec/cm 2
1 ubar-sec
14 XlO~ 6 psi-sec
Material that provides protec-
tion from the thermal
environment radiation and
fireball immersion of nuclear
weapon explosions.
Tripartite Technical Coopera-
tion Programme. Member
nations are Canada, the United
Kingdom, and the United
States, s.
A description of the expected
nuclear attack, including num-
ber of weapons, their yields,
burst conditions, and timing of
their detonation.
A function relating free-field
nuclear weapon-effect
environments to local loads on a
system or system element.
Two-Sided
Procedure:
Type I Error:
Type I! Error:
Uncertainty:
Variance:
Weapon Range:
A statistical test wherein the
hypothesis is accepted if the
statistic falls between limits,
i.e., ti <t <t 2 , in contrast to a
one-sided procedure where the
statistic must satisfy an
inequality of the form t <ti (or
t >t 2 ).
Statistical probability of reject-
ing a hypothesis when it is true,
i.e., an a error.
Acceptance of a hypothesis as
true on statistical grounds when
it is false, i.e., a B error.
The amount (estimated) by
which the predicted value may
vary from the observed or true
value.
The square of the standard de-
viation; for a finite sample the
variance (S 2 ) is defined by
N
N-l
i=n
The horizontal distance from
the burst point to the target
point, also called the "offset."
The distance between burst
point and target point is the
slant range.
t Statistic:
A statistic for comparing the
sample and population means
when the standard deviation is
unknown.
Glossary-5
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